Modeling Interaction of a Tropical Cyclone with Its Cold Wake

Sue Chen Naval Research Laboratory, Monterey, California

Search for other papers by Sue Chen in
Current site
Google Scholar
PubMed
Close
,
Russell L. Elsberry University of Colorado Colorado Springs, Colorado Springs, Colorado

Search for other papers by Russell L. Elsberry in
Current site
Google Scholar
PubMed
Close
, and
Patrick A. Harr Department of Meteorology, Naval Postgraduate School, Monterey, California

Search for other papers by Patrick A. Harr in
Current site
Google Scholar
PubMed
Close
Open access

Abstract

This study first examines the tropical cyclone (TC) intensity response to its cold wake with time-invariant, stationary cold wakes and an uncoupled version of COAMPS-TC, and second with simulated cold wakes from the fully coupled version. The objective of the uncoupled simulations with the time-invariant cold wake is to fix the thermodynamic response and to isolate the dynamic response of the TC to the cold wake. While the stationary TC over a cold wake has an immediate intensity decrease, the intensity decrease with a long trailing wake from the moving TC was delayed. This time delay is attributed to a “wake jet” that leads to an enhanced inward transport of moist air that tends to offset the effect of decreasing enthalpy flux from the ocean. In the fully coupled version, the TC translating at 2 m s−1 generated a long trailing cold wake, and again the intensity decrease was delayed. Lagrangian trajectories released behind the TC center at four times illustrate the inward deflection and ascent and descent as the air parcels cross the trailing cold wake. The momentum budget analysis indicates large radial and tangential wind tendencies primarily due to imbalances among the pressure gradient force, the Coriolis, and the horizontal advection as the parcels pass over the cold wake. Nevertheless, a steadily increasing radial inflow (wake jet) is simulated in the region of a positive moisture anomaly that tends to offset the thermodynamic effect of decreasing enthalpy flux.

Denotes content that is immediately available upon publication as open access.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sue Chen, sue.chen@nrlmry.navy.mil

Abstract

This study first examines the tropical cyclone (TC) intensity response to its cold wake with time-invariant, stationary cold wakes and an uncoupled version of COAMPS-TC, and second with simulated cold wakes from the fully coupled version. The objective of the uncoupled simulations with the time-invariant cold wake is to fix the thermodynamic response and to isolate the dynamic response of the TC to the cold wake. While the stationary TC over a cold wake has an immediate intensity decrease, the intensity decrease with a long trailing wake from the moving TC was delayed. This time delay is attributed to a “wake jet” that leads to an enhanced inward transport of moist air that tends to offset the effect of decreasing enthalpy flux from the ocean. In the fully coupled version, the TC translating at 2 m s−1 generated a long trailing cold wake, and again the intensity decrease was delayed. Lagrangian trajectories released behind the TC center at four times illustrate the inward deflection and ascent and descent as the air parcels cross the trailing cold wake. The momentum budget analysis indicates large radial and tangential wind tendencies primarily due to imbalances among the pressure gradient force, the Coriolis, and the horizontal advection as the parcels pass over the cold wake. Nevertheless, a steadily increasing radial inflow (wake jet) is simulated in the region of a positive moisture anomaly that tends to offset the thermodynamic effect of decreasing enthalpy flux.

Denotes content that is immediately available upon publication as open access.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sue Chen, sue.chen@nrlmry.navy.mil

1. Introduction

Improved understanding of how the ocean modulates TC intensity and track changes is needed to better observe, assimilate, and forecast TC intensity. Progress in understanding the upper-ocean processes and air–sea interaction during the passage of TCs has been summarized in a review article by Shay (2010). It is well established that the formation of the ocean cold wake is a result of wind mixing, upwelling, and horizontal advection. Each of these forcing mechanisms operates in a different region of the ocean under the TC. While the upwelling is predominantly under the eye, the wind-mixing regime extends to outer radii with the maximum extent to the right of the track in the Northern Hemisphere. Horizontal advection by the ocean currents moves cold water from the rear part of the wake to the front and extends the width and asymmetric distribution of the wake (Chen et al. 2010: Vincent et al. 2012). These advective effects on the TC wake are difficult to document from observations because of the high winds and waves under the TC.

Chang and Anthes (1978) and Price (1981) studied the location of the cold wake relative to the TC center due to a translating TC using both prescribed symmetric and asymmetric TC wind forcing with three-dimensional ocean models and for various TC translation speeds. Both of these modeling studies demonstrated the rightward bias of the wake location with respect to the TC track in the Northern Hemisphere arises as a result of the TC translation or as a result of the asymmetric wind forcing. That is, the near-resonant effect of the wind stress and the ocean currents cause the cold wake to be stronger to the right of the TC track. Price (1981) also showed that given the same initial TC stress forcing, the rightward shift of the cold wake is reduced (but the magnitude is increased) with smaller TC translation speeds. A near-symmetric wake about the TC track was obtained with a very slow translation speed of 2 m s−1, but then significant upwelling is also expected with such a slow translation speed.

Cione and Uhlhorn (2003) summarized sea surface temperature (SST) decreases in observations from 33 Atlantic TCs using the airborne expendable bathythermographs (AXBTs) or moored buoys. In the TC inner-core region (60 km), the SST decreases were on the order of 0°–2°C, which is about one-half of the 4°–5°C decreases in outer radii (<200 km). The inner-core SST decreases are smaller for lower-latitude and faster-moving TCs because of the deeper and warmer prestorm upper-ocean environment at the lower latitudes, and the faster translation speeds lead to shorter ocean response times. In the inner core, the radius of maximum SST decrease is about 1.2° latitude. Because of the high wind speeds in the TC inner core, even a moderate 1°C decrease in the inner-core SST may reduce by about 40% the enthalpy flux transfer from the ocean to the TC. These observational results of Cione and Uhlhorn (2003) are consistent with the model results of Price (1981). Thus, reducing the SST below the inner-core region of the TC is an effective thermodynamic pathway to reduce the TC intensity.

To further examine the ocean feedback in strong TCs, a survey is conducted of some key studies of the cold-wake magnitudes associated with category-3–5 TCs. Shay et al. (1992), D’Asaro et al. (2007), Jaimes and Shay (2009), and Sanford et al. (2011) found the largest SST decreases were mostly in the outer radii in the rear-right quadrant relative to the TC center. Large 4°–5°C decreases were detected in the Hurricanes Felix, Ivan, Katrina, and Rita. By contrast, category-4 Hurricane Frances and category-3 Typhoon Fanapi had more moderate 1°–3°C cooling (D’Asaro et al. 2007; Sanford et al. 2011; Mrvaljevic et al. 2013). The Hurricane Frances cold wake was primarily in the outer radii and the wake magnitude in the inner-core region was only 1°–2°C. In general, these results are within the range of SST decreases described by Cione and Uhlhorn (2003).

As indicated above, the magnitude of the cold wake is primarily determined by the ocean-current-induced mixing at the base of the mixed layer and the upwelling under the TC eye. However, the wake magnitude may be modulated by the effects of precipitation (Jacob and Koblinsky 2007; Balaguru et al. 2012) and by wind–wave–current interactions (Doyle 2002; Sullivan et al. 2012; Liu et al. 2011; Lee and Chen 2012; Smith et al. 2013). Colder wakes are enhanced over a preexisting cold eddy and with a shallow mixed layer (Price 1981; Jacob and Shay 2003; Lin et al. 2008; Wu et al. 2007; Jaimes and Shay 2009, 2010; Ma et al. 2013).

Numerous studies have suggested that TC intensity change is positively correlated with the prestorm upper-ocean thermal structure (e.g., Lin et al. 2008, 2009). Studies of the ocean feedback to TC intensity change have focused on the thermodynamic pathway through calculations of the reduction of surface enthalpy flux transfers from the ocean to the TC. Consequently, the TC intensity is decreased with a larger-magnitude cold wake, while the TC intensification is favored over a region of higher ocean heat content.

A dynamic pathway of the cold wake on the TC circulation was first demonstrated with a simple idealized hurricane model (Zhu et al. 2004) and subsequently confirmed by a full-physics coupled simulation of Hurricane Katrina (Chen et al. 2010). Using the ocean-coupled version of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS), Chen et al. (2010) demonstrated the cold wake induced a broadening of the inner-core TC circulation, but not in the outer region, and the largest convergence in the boundary was cyclonically shifted to downwind of the cold wake. In addition, the equivalent potential temperature was decreased in the inner core but was increased in the outflow region compared to the uncoupled COAMPS integration. Both Zhu et al. (2004) and Chen et al. (2010) as well as a recent Lee and Chen (2014) study indicated an increased asymmetry in the simulated TC vortex. Lee and Chen (2014) demonstrated that the increase in TC asymmetry due to its cold wake was associated with the reduction of the atmospheric mixed-layer depth and the depth of the atmospheric inflow layer in the TC quadrant over the cold wake. Although the mechanism(s) by which the wake affects the TC transverse circulation is (are) not well understood, Lee and Chen (2014) suggested that an enhanced low-level inflow would transport warm and moist air into the inner-core region.

Despite a large body of literature that discusses the TC structure and intensity changes owing to air–sea interaction, or describes the ocean response to a passing TC, two key questions need to be further studied: 1) How does the location relative to the TC center and the shape of the cold wake affect the TC intensity change during the storm intensification stage? 2) What are the key physical processes in the TC response to the cold wake during the storm stage?

Given the complexity of isolating the governing physical processes in a full-physics coupled model, a simpler and controlled framework will be utilized in this study to further document the dynamic impact of the ocean cold wake described by Chen et al. (2010) and to investigate the intensity and structure changes as the TC circulation crosses its cold wake. To first isolate this dynamic pathway versus the thermodynamic pathway, idealized coupled COAMPS-TC model-simulated category-3–5 TCs are examined in an ocean-cold-wake parameter space that includes the cold-wake magnitude, shape, and location. Whereas the COAMPS-TC model used in this study has been extensively described in Chen et al. (2010), only the modifications of the model for these idealized cold wakes under a stationary TC will be described in section 2. The simulated TC dynamic responses to three cold wakes with various magnitudes, shapes, and locations are examined in section 3. In section 4, these controlled/idealized conditions are relaxed to allow nonlinear two-way interaction with the flow response under the storm motion in fully coupled air–ocean experiments. Section 5 provides a summary of these idealized and fully coupled experiments to document the additional dynamic pathway in the response of the TC to its cold wake.

2. COAMPS-TC model description and experiment setup

A somewhat simplified version of the coupled COAMPS-TC system is used. The atmospheric component and the suite of atmospheric physics are described in Doyle et al. (2012). The atmospheric physics include the Fu–Liou four-stream radiation scheme (Liu et al. 2009) and the Mellor–Yamada (Mellor and Yamada 1974) level-2.5 turbulent kinetic energy (TKE) closure mixing scheme. For wind speeds greater than 27 m s−1, the uncoupled and air–ocean-coupled momentum drag coefficient asymptotically approaches a value of 0.025, which is similar to the value in Powell et al. (2003). The air–ocean coupling between the atmosphere and ocean is described in Chen et al. (2010). Because the focus of this study is on the dynamic response to the cold wake, a recent update to the fully coupled air–ocean–wave COAMPS-TC system for ocean–wave interaction (Smith et al. 2013) is not used for this study to reduce the complexity of the air–sea interaction physics. The ocean component is the Navy Coastal Ocean Model (NCOM; Martin 2000). A fine vertical spacing (0.5 m) is used in the upper 10 m to resolve the diurnal cycle.

a. Idealized TC initialization

A three-dimensional axisymmetric TC circulation is generated in COAMPS-TC to set up simplified conditions to first isolate the dynamic mechanism in the TC–cold wake interaction. While numeric and physics options are the same as in the operational COAMPS-TC, the TC vortex is spun up based on a user-specified initial tropical environment sounding instead of using an initial bogus vortex. The spinup process starts with an initial vortex with a low-level wind speed maximum of 25 m s−1 at 90 km and decreasing to zero wind at 240 km. During the spinup period, the surface friction forces low-level convergence and upward vertical motion within the radius of maximum winds, and the model mass fields adjust to the winds due to the convective heating. The initial environment wind profile in which the TC vortex is embedded is also user specified.

In the fixed-wake experiments, the basic flow is at rest with a prescribed time-invariant two-dimensional cold wake and compared with the uncoupled control (CNTL) experiment that has a uniform, time-invariant SST. Furthermore, the effect of environmental vertical wind shear are not considered in this set of experiments. A mean wind speed is subtracted from the model winds to counter the movement of the simulated TC and thus keep the TC quasi stationary close to the center of the model domain with no motion-induced asymmetry in the wind field. All model simulations are on an f plane, so no beta-effect propagation is present. These idealized conditions and controls on the TC assist in isolating the dynamic response to the cold wake from the response due to the thermodynamic pathway. A digital filter (Lynch and Huang 1992) with a 2-h integration time window is applied prior to the start of the model integration to ensure the wind and mass fields in the initial idealized vortex are balanced. The coarse domain has a radiative lateral boundary condition to allow the inertia–gravity waves excited by the convection to propagate out of that domain. The radiative forcing at all grid points is calculated at 20°N, 120°E, which eliminates the differential radiative forcing in either the latitudinal or longitudinal direction. A forward-in-time integration scheme is used for all model scalar fields. A hybrid forward time-stepping option in COAMPS-TC is found to perform better in preserving the sharp gradients in the model than did the leapfrog option.

The initial atmospheric thermodynamic profile for all experiments is from the Gray et al. (1975) composite-mean nighttime tropical cloud-cluster sounding over the western North Pacific (Table A1 and Fig. A1). While this Gray et al. mean temperature profile extends to 80 hPa, the relative humidity profile only extends to 400 hPa, so the initial mixing ratios above that level are set to zero. Since the model top is much higher than the Gray mean cloud-cluster sounding, the temperature above 80 hPa is assumed to be isothermal—that is, the value at 80 hPa. Compared to the Jordan (1958) mean sounding, the Gray mean cloud-cluster sounding is slightly warmer in the midtroposphere above 600 hPa. The Gray mean sounding moisture above 900 hPa is also much larger than in the Jordan (1958) or the Dunion and Marron (2008) non–Saharan air layer sounding.

For the atmosphere–ocean two-way coupled experiment, the initial ocean temperature and salinity profiles are shown in the appendix (Table A2 and Fig. A2). These profiles are based on a composite of six surface and subsurface moorings from the Impact of Typhoons on the Ocean in the Pacific (ITOP) field experiment during 14–16 September 2010 prior to the passage of Typhoon Fanapi. The salinity profiles above 130 m and below 500 m are extrapolated from the composite. The pre-Fanapi composite has a SST close to 30°C (i.e., about the same magnitude as in the uncoupled control run), a mixed layer depth of 60 m, and a 1.3 kJ ocean heat content integrated to a depth of 100 m (Price 2009). While a quiescent initial ocean is specified, currents are forced by the TC wind stress.

b. Axisymmetric fixed-wake experiments

The numerical experiments include uncoupled, fixed-wake, and two-way air–ocean coupled model configurations (Table 1). The CNTL and all fixed-wake experiments have the atmospheric model top at around 29 km. The three model domains consist of coarse mesh with 9-km horizontal spacing, medium nest 2 at 3-km spacing, and inner nest 3 at 1-km spacing. The 70 sigma levels have vertical spacing of 20 m in the lowest 560 m and then gradually increasing to 1000 m at the top four model levels. The CNTL and fixed-wake experiments are designed to systematically quantify the dynamic response of the TC to its cold wake. This dynamic response in the TC flow fields is first studied by comparing simulations with and without the SST cold anomaly. In these idealized cold wake simulations, the simulated TC is first spun up to category-4 strength at 36 h, and then a prescribed cold wake is inserted and held constant to the end of the 72-h simulation. Although such an instantaneous switch-on of the cold wake at 36 h causes an imbalance in the model, the shock to the simulated TC is quickly adjusted in the model.

Table 1.

List of three sets of numerical experiments with experiment name, brief description, and the horizontal grid spacing in the atmospheric model.

Table 1.

The CNTL experiment has a horizontally uniform SST of 303 K that is also invariant in time. The first set of time-invariant wake experiments is then performed to examine the TC response to the locations, shapes, and magnitudes of the prescribed cold wakes. A total of five ocean-cold-wake configurations were examined in Chen (2014). Because the most interesting comparisons are from the circular-shape wakes underneath the eyewall versus the oval-shape trailing cold wake, subsequent discussions will be focused on only three experiments (Fig. 1): wake 1 with a 2°C circular-shape cold anomaly, wake 2 also with a circular shape but with a 4°C cold anomaly, and wake 3 with an oval-shape 2°C cold anomaly. For the interested reader, discussions of a half-circle wake and a crescent-shape wake are provided in Chen (2014).

Fig. 1.
Fig. 1.

Schematic illustration of the ocean-cold-wake-1–wake-3 sensitivity experiments: (a) a circle-shape wake 1 (2) with a 2° (4°)C cold anomaly centered under the TC at x = 250 km, y = 250 km and (b) an oval-shape wake 3 that is 270 km in length and is located to the right rear of the TC center that is at the same position as in wakes 1 and 2. The yellow circle depicts the uncoupled CNTL radius of maximum wind.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

The wake-1 and wake-2 experiments represent special cases of the TC remaining stationary and interacting with cold wakes generated under the eyewall with 2°–4°C SST anomalies that have been reported in the literature (Cione and Uhlhorn 2003; Mrvaljevic et al. 2013). The wake-3 experiment is intended to represent a TC moving away from, but still interacting with, the cold wake that it had generated. While the TC is again not moving in the wake-3 experiment, the SST pattern is also fixed in space and time so that a minimal direct negative feedback effect on the intensity is expected. Thus, the focus is more on the intensity and structure changes of the TC circulation due to the interaction with the trailing cold wake, rather than due to the direct influence of the leading portion of the wake 3 that is under the eyewall.

c. Two-way coupled atmosphere–ocean experiments

The two-way interaction of the TC with the ocean is simulated with the atmosphere–ocean coupled COAMPS-TC. For these coupled experiments, the atmospheric model inner-nest horizontal grid spacing is 3 km. The ocean model domain has a horizontal grid spacing of 3 km, and has 51 vertical layers, with 20 layers in the upper 100 m of ocean A stationary (0 m s−1, EXPA) and a moderate (2 m s−1, EXPB) westward-moving storm translation speed are used to simulate trailing cold wakes similar to the wake-1 and wake-3 experiments. In addition, fixed SST experiments with the same translation speed as EXPA and EXPB are also conducted (EXPAunc and EXPBunc) to quantify the effect of two-way coupling. The early Chang and Anthes (1978, 1979) and Price (1981) uncoupled ocean model experiments with less complicated coupled atmospheric and oceanic models have shown a slow (faster) TC translation speed leads to a larger (smaller) magnitude cold wake response. In additional to the TC translation speed, the magnitude of the cold wake also is affected by the initial upper-ocean stability and mixed layer depth (Lin et al. 2008).

The atmospheric model is first integrated for 36 h without the air–ocean coupling, which allows for the simulated TC to generate a stationary or a trailing ocean cold wake to develop underneath the eyewall and in the rear-right quadrant along the model-simulated TC track, respectively. After 36 h, the two-way coupling is turned on with a coupling interval of 2 min. Since the ocean feedback to the atmosphere interaction is not turned on until 36 h (i.e., the model atmosphere is not previously responding to the ocean cold wake), this procedure allows the spinup of the model-simulated TC to category-3–5 intensity without the influence of the cold ocean wake. The sudden exposure of the model TC to the ocean-cold-wake experiments is analogous to a real-world TC that had been moving rapidly but then suddenly slows down and quickly induces a cold wake.

3. Control and time-invariant wake experiments

a. Fixed-SST control simulation

The intensification of the TC in the CNTL experiment takes more than a day. The maximum wind speed increases rapidly from Saffir–Simpson category (CAT) 1 at 12-h forecast time to a CAT5 by 42 h. After 42 h, the maximum wind speed oscillates between 80 and 95 m s−1. The maximum wind speed and minimum sea level pressure (MSLP) at 72 h are 95 m s−1 and 936 hPa, respectively. This high TC intensity is expected since no environmental vertical wind shear is imposed in the CNTL experiment. One effect of vertical wind shear is to decrease the TC intensity by inducing a vertical tilt of the vortex in the downshear-left direction (Jones 1995, 2000a,b: Frank and Ritchie 1999). With no background vertical wind shear, any vertical tilt of the CNTL vortex may then be attributed to the local shear produced by internal vortex dynamics (Wong and Chan 2004). During the CAT3-to-CAT5 stage intensification, the magnitude of the vortex tilt below 5-km height is small (~4 km in the horizontal). Indeed, the vorticity maxima at 400 and 850 hPa are almost vertically aligned throughout the 72-h integration (not shown).

Although the idealized TC vortex is three dimensional, its structure is designed to be symmetrical about the center. Thus, the kinematic and thermodynamics fields in the CNTL experiment may be displayed as azimuthal means at each forecast time. A time average of the azimuthal-mean fields is calculated over 36–72 h, which is the time period during which the TC spins up to CAT3–CAT5 intensity. In these composites, the abscissa is normalized with the mean radius of maximum tangential wind (RMW), which has a value of 21 km at 10-m height.

Chen (2014) compared the model-simulated TC structure during the CAT3–CAT5 intensity period with the Doppler radar composites of axisymmetric wind structure from eight CAT 3–5 Atlantic hurricanes (Rogers et al. 2012, see their Figs. 7, 8, and 11). The CNTL composites of tangential wind, low-level inflow,vertical velocity, vorticity, and TKE structure were remarkably similar to the composites from the airborne Doppler radar.

b. Idealized wake experiments

Comparisons of the circular wake-1 and wake-2 experiments with the elongated wake-3 experiment (Fig. 1) are used to test hypothesis 1: “A cold wake centered underneath the TC core has more immediate thermodynamic and dynamical impacts on the TC intensity than a trailing cold wake.” The symmetric versus asymmetric wake-shape experiments are used to test hypothesis 2: “In a certain region of moderate winds outside the radius of maximum wind, the ocean cold wake forces a low-level atmospheric wake jet that is deflected toward the center of the storm.”

The axisymmetric structure is defined in composites of the azimuthal-mean fields as displayed for the CNTL experiment. The time evolutions of maximum wind speed Vmax and MSLP from the CNTL and the wake experiments are similar prior to the switching on the coupling with the wake at 36 h (Fig. 2). The Vmax difference between the CNTL and the wake experiments is less than 10 m s−1 at 36 h when the coupling with the cold wakes is initiated (recall that these idealized wakes are fixed in time from 36 to 72 h). Since the intensities at end time in all of the wake experiments are considerably lower than for the CNTL experiment, these initial intensity differences at 36 h do not alter the interpretation of the overall TC responses to the wake-1, wake-2, and wake-3 cold anomalies.

Fig. 2.
Fig. 2.

Comparison of the (a) maximum wind speeds (m s−1) and (b) minimum sea level pressures (hPa) between the CNTL and the wake-1–3 experiments, in which the coupling begins instantaneously at hour 36. See the keys for the line definitions for the wake experiments.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

At 36 h when the cold wakes are inserted the simulated TC is at CAT4 intensity. The wake-1 experiment with a 2°C circular cold anomaly results in at least one hurricane-intensity-category decrease compared to the CNTL (Fig. 2a). Inserting the 4°C circular cold anomaly in the wake-2 experiment causes an almost immediate and then a sustained decrease in intensity to CAT1 at 72 h. The corresponding MSLP rise in the wake-1 experiment is from 963 hPa at 36 h to 981 hPa at 45 h and then a redeepening due to diurnal heating with a MSLP of about 962 hPa at 72 h. With the 4°C cold anomaly under the TC center in the wake-2 experiment, the MSLP rises steadily to 995 hPa at 72 h.

Whereas the wake-3 experiment also has a 2°C cold anomaly and has about the same areal extent as wake 1, this cold wake extends behind the center and so the TC intensity continues to increase and reaches the same upper-CAT5 intensity as the CNTL around 48 h (Fig. 2a). The TC delayed intensity from the trailing cold wake has been noted in observations (Mainelli-Huber 2000). The thermodynamic pathway explanation for the decrease in Vmax (Fig. 2a) and a rapid increase in MSLP (Fig. 2b) is that the inner-core circulation that passes over the trailing cold wake then wraps around the center and enters the eye region with a lower equivalent potential temperature. However, the dynamic pathway explanation explored here is that the effect of the 2°C cold wake 3 under the TC does not decrease the intensity as rapidly as say wake 1 (that also is a 2°C cold wake) might suggest because of inward turning of the airstream over the cold wake that enhances the inward flux of moist air. The MSLP rise ends around 56 h, and the TC circulation is then in equilibrium with the trailing wake by 72 h with a MSLP = 957 hPa.

This set of experiments, which was designed to answer question 1 in the introduction regarding the shape and magnitude of the cold wake relative to the TC center, provides some hints that the cold wake underneath the eyewall region (especially wake 2 with a 4°C cold anomaly) is more efficient than a trailing wake in spinning down the TC. The following sections will explore thermodynamic responses as well as question 2 in the introduction regarding the dynamic response and processes that lead to delayed intensity changes.

c. Thermodynamic pathway

The primary thermodynamic factor that impacts the TC intensity from the wake cooling is the reduction of the enthalpy flux transport from the ocean. The almost immediate decrease in Vmax at 36 h for wake 1 (wake 2) with a 2° (4°)C cold anomaly inserted under the TC center is due to the reduction in enthalpy flux so that deep convection in the eyewall (which is at a small radius for a CAT4 TC at 36 h) cannot be maintained. Thus, the eyewall must reform at the outer edges of cold wakes 1 and 2 where the MSLP deviation from the environmental value will be smaller and the cyclostrophic (υ/r) contribution to the vortex balance will be smaller. Since wake 3 is in the right-rear quadrant of the TC, the reduction in enthalpy flux over the 2°C cold anomaly does not have an immediate impact on the equivalent potential temperature θE of the air particles entering the eyewall. However, the air parcels crossing the trailing wake at larger radii behind the center, which will encounter reduced enthalpy fluxes while passing over the cold wake, will wrap around the center and eventually enter the eyewall with a lower θE value than if the cold wake had not been present. The magnitude by which the θE is lowered depends on the fraction of the time that the air parcel has spent over the cold wake and any modification of the enthalpy flux during the remaining time the air parcel was passing over warmer water.

The magnitudes of the enthalpy fluxes from the ocean are of course also related to the surface wind speed. Thus, the enthalpy fluxes are calculated both within the area inside the RMW and within 200 km (Fig. 3). Within the RMW, the CNTL and wake 3 have the same amount of ~7 × 104 W m−2 enthalpy fluxes, and even within 200 km the enthalpy fluxes in the wake-3 experiment are only decreased 11% relative to the CNTL. Only the wake-2 experiment with a 4°C cold anomaly has a substantial decrease within the RMW (5.2 × 104 W m−2). Whereas the CNTL has the largest total flux of 16 × 104 W m−2 within 200-km radius, the total fluxes in the wake 1, wake 2, and wake 3 experiments are around 12, 9, and 14 × 104 W m−2, respectively. The enthalpy flux difference within 200 km is a 23% reduction between the wake-1 and wake-2 experiments that have the same area of a cold wake directly below eyewall, and anomalies of 2° and 4°C, respectively. This flux difference is primarily due to the reduction in surface winds and the air–sea temperature and humidity differences associated with the large decrease in intensity in the wake-2 experiment relative to wake 1 (Fig. 2a).

Fig. 3.
Fig. 3.

Total enthalpy flux (104 W m−2) within the RMW (cyan bar) and within 200-km radius (blue bar) at 42–54 h for the CNTL and wake-1–3 experiments. The white and blue numbers above each cyan and blue bars are their corresponding total enthalpy flux (104 W m−2).

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

In summary of the thermodynamic pathway, the equilibrium intensity decreases relative to the CNTL at 72 h (Fig. 2a) are proportional to the decreases in the total enthalpy fluxes within 200 km in the wakes-1–3 experiments relative to the CNTL (Fig. 3). This result confirms the thermodynamic aspect of hypothesis 1 that a cold wake underneath the TC core has the larger impact on the TC intensity than a trailing cold wake. The next section examines the impacts of these cold wakes on the dynamic pathway.

d. Dynamic pathway

Comparing the intensity changes in the CNTL with those on the wake experiments, the differences in cold wake areas that are under the eyewall suggest a dynamic response that delays the TC spindown (Fig. 2). Specifically, the trailing oval wake 3 has a prolonged adjustment time for TC spindown. These simulations suggest a more complicated TC dynamic response to the cold-wake forcing in addition to the direct thermodynamic impact in the early studies of Emanuel (1986) and Bender and Ginis (2000). These wake experiments have been designed to link differences in intensity responses to a dynamic pathway that contributes to a time delay in the TC spindown.

While introducing these cold wakes forces an asymmetric response in the TC structure, that aspect of the response is the topic of a future article. Rather, the TC structure changes from the symmetric (wakes 1 and 2) and asymmetric (wake 3) cold wakes will be via the comparisons of axisymmetric composites relative to the structure in the CNTL. These composites are calculated between 42 and 54 h, which begins 6 h after the time the cold wake is introduced to avoid the initial period of shock in the model.

The horizontal and vertical structures of the tangential wind are also affected with the interaction with the cold wake (Fig. 4a). For example, the RMWs (at 10 m) in the CNTL, wake-1, and wake-2 experiments are relatively similar at 21, 27, and 29 km, respectively. By contrast, the vertical tilts of the RMW for the wake-1 and wake-2 experiments are much larger (doubled and almost tripled radii at 10-km elevation compared to the RMW at 10-m elevation) than the almost vertically oriented RMW for the CNTL. For wake 3 with the long trailing cold wake, the RMW tends to be vertically upright as in the CNTL. Whereas the vertical extent of the maximum tangential winds in the wake-3 experiments is also similar to the CNTL, the TC vertical extents for the wake-1 and wake-2 experiments are much reduced, which is attributed to weaker vertical extent of convection since the eyewall is directly over these cold wakes.

Fig. 4.
Fig. 4.

Composites of the azimuthal-mean tangential wind speed (contour interval: 5 m s−1) at 42–54 h from (a) CNTL, (b) wake-1, (c) wake-2, and (d) wake-3 experiments. Black line represents the RMW at each level.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

The corresponding azimuthal-mean profiles of radial wind in the wake experiments compared to the CNTL experiment (Fig. 5) illustrate the differences in the secondary circulation. Whereas the maximum near-surface inflow is 15 m s−1 in the CNTL, it is reduced to 12 m s−1 in the wake-3 experiment with a trailing cold wake. By contrast, the wake-1 and wake-2 experiments with cold wakes directly under the eyewall have reductions in the maximum low-level radial inflows to 8.8 and 8.3 m s−1, respectfully. These reductions are a maximum inside the RMW, which is consistent with the larger reductions in intensity for the wake-1 and wake-2 experiments (36 and 35 m s−1 vs 52 m s−1 in the CNTL). The upper-level outflows in the secondary circulations are also reduced. Dramatic reductions in the magnitudes of the outflow, and the elevations of the outflow, are noted for the wake-1 and wake-2 experiments. Interestingly, the outflow in the wake-2 experiment is stronger than in the CNTL, even though there is a rapid reduction of intensity and a decreased low-level inflow. With the insertion of the very cold wake 2 directly underneath the eyewall, the MSLP rises more rapidly and continues to rise through the remainder of the integration (Fig. 2b). Consequently, the radial pressure gradients of all elevations are rapidly decreasing in the wake-2 experiment. In particular, the wind–pressure relationship in the outflow layer is continually out of balance such that the outflow can be sustained, or even increased, through the 42–54-h period (Fig. 5c).

Fig. 5.
Fig. 5.

As in Fig. 4, but for the azimuthal-mean radial wind components (contour interval: 2 m s−1). The maximum low-level radial inflow wind speeds for CNTL, wake 1, wake 2, and wake 3 are 15, 8.8, 8.3, and 12 m s−1 respectively. (e) A zoomed-in view of (d) in the lowest 2 km.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

An important aspect of the trailing-wake-3 experiment (Fig. 5d) is the larger radial inflow in the lower troposphere at radii >4RMW than the CNTL (Fig. 5a), and especially relative to the wake-1 (Fig. 5b) and wake-2 (Fig. 5c) experiments. This enhanced inflow is the dynamical pathway that has important implications, including contributing to a larger inward flux of moisture (not shown), which will be further discussed in section 4.

In the wake-1 (Fig. 6b) and wake-2 (Fig. 6c) experiments with the TC center over the circular cold wakes, the radial pressure gradients near the RMW are considerably decreased and the vertical extents are much smaller compared to CNTL (Fig. 6a). Comparing the radial pressure gradients in the wake-3 experiment (Fig. 6d) relative to the CNTL (Fig. 6a) indicates the wake-3 experiment has a somewhat smaller radial pressure gradient near the RMW. From gradient wind balance considerations, the reductions of momentum flux divergence in the TC outer radii in the trailing-wake-3 experiment should be balanced by changes in the pressure gradient and the tangential and radial wind speeds compared to the CNTL experiment.

Fig. 6.
Fig. 6.

Composites of the azimuthal-mean radial pressure gradients (hPa km−1) from (a) CNTL, (b) wake-1, (c) wake-2, and (d) wake-3 experiments at 42–54 h.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

In summary, the first set of time-invariant wake experiments demonstrates the following: (i) reductions in the TC intensity from the cold wakes directly under the TC eyewall occur earlier and are larger than in the trailing-wake experiment; (ii) a cold wake under the inner-core region modifies the secondary circulation with a decreased inflow, a larger outward tilt of the eyewall, and a shallower outflow at a lower elevation; and (iii) while the trailing cold wake 3 induces a smaller secondary circulation than in the CNTL, the inflow branch of the secondary circulation is enhanced at outer radii in such a way as to bring moisture into the inner core. This modified secondary circulation is proposed to be the dynamic pathway to account for the delayed weakening in the wake-3 experiment. While this feature has been isolated here in a time-invariant wake experiment, this feature will be further examined in a fully coupled model in section 4.

4. Effect of the two-way nonlinear air–sea interaction

In nature, the TC interaction with the ocean changes continually, and this interaction is nonlinear. To reexamine the hypothesis 1 from section 3b, two-way coupling is simulated from two coupled wake experiments with the NCOM model and compared with uncoupled control experiments with fixed SST (Table 1).

At 42 h (Fig. 7), EXPA and EXPB have maximum cold anomalies of −7.8° and −2.5°C, respectively. Note the shape and magnitudes of the EXPB cold anomalies are similar to the wake-3 experiment discussed in section 3. The EXPB experiment has a longer trailing cold wake owing to a moderate translation speed (2 m s−1). These simulations are also consistent with the early TC cold-wake studies of Chang and Anthes (1978) and Price (1981) and illustrate again that the TC translation speed is one of the major factors that controls the magnitude and location of the trailing cold wake with respect to the TC track given the same upper-ocean density profile.

Fig. 7.
Fig. 7.

Sea surface temperature anomalies (°C; color scale on the right) and 10-m wind stress (m2 s−2; red contours, interval: 0.001 m2 s−2) near the model-simulated TC at 42 h from simulations (a) EXPA with a 0 m s−1 westward translation speed and (b) EXPB with a 2 m s−1 westward translation speed. The 10-m wind stress (red) and current (black) vectors are plotted every two grid points.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

To provide a comparison between these fully coupled and the noncoupled wake experiments discussed in section 3, uncoupled EXPA (unc EXPA) and EXPB (unc EXPB) integrations are also prepared (Table 1). A larger cold-wake magnitude under the eyewall results in a smaller TC intensity in the coupled experiments. The azimuthal-mean maximum 10-m wind speeds between 42 and 52 h from the EXPA, unc EXPA, EXPB, and unc EXPB simulations are 40, 52, 49, and 52 m s−1, respectively. Again, it is noteworthy that the EXPB (trailing wake) intensity decrease does not occur immediately as in the EXPA (stationary wake). Rather, the intensity decrease is delayed by almost 12 h after the simulated TC first experienced the cold wake at 36 h, which is consistent with the 14-h time delay of the intensity decrease from the wake-3 experiment described in section 3 (Fig. 3).

Two other aspects of the composites of these two-way coupled experiments versus their noncoupled simulations are similar to the wake experiments versus the CNTL discussed in section 3. First, the EXPB cold wake induces a broad area of anomalous surface inflow (Fig. 8a) and a concentrated region of moistening above the boundary layer out to near 10 times the RMW (Fig. 8b). In this two-way coupled EXPB simulation, the enhanced low-level radial inflow extended beyond 10RMW, which is farther out compared to all of the wake experiments in section 3 owing to the longer trailing cold wake (Fig. 7b). Notice also that the moist air appears to be lifted inward of about 6RMW. Just as the wake-3 experiment in section 3 also had anomalous moistening in and above the TC boundary layer, it is this combination of an enhanced radial inflow and anomalous moist air that is hypothesized to have sustained the intensity of the TC during this 42–54-h period against the negative thermodynamic feedback of the trailing wake. This effect is larger in the elongated cold wake 3 and EXPB than in the broader cold wake 1 and EXPA (not shown).

Fig. 8.
Fig. 8.

(a) Composite radial wind speed (m s−1; interval: 1 m s−1, negative values denote inflow) and (b) mixing ratio (kg kg−1; interval: 0.5 × 10−4 kg kg−1) anomalies at 42–54 h for the EXPB relative to the unc EXPB. Black dotted line represents the RMW at each level scaled by the RMW (16.5 km) at the 10-m height level.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

The intensity changes in these two-way coupled experiments are due to the cumulative thermodynamic and dynamic effects of the TC interacting with its cold wake, which includes the nonlinear interaction via the two-way coupling with the model physics. A key agreement between these two-way coupled responses and the time-invariant wake experiments is that both the magnitudes of cold wake underneath the eyewall and the aspect ratio (width/length) of the trailing cold wake modulate the TC intensity. This sensitivity of the TC intensity to the aspect ratio of the cold wake has not been previously discussed in the literature.

a. Lagrangian trajectory analysis

A second objective in this section is to describe the origin of a “wake jet” as the low-level airstream in the TC circulation passes over its cold wake. Chen et al. (2010) first proposed the existence of a wake jet as the warm, moist airstream interacts with the cooler air over the ocean cold wake that has been modified by air–sea fluxes. Recently, Lee and Chen (2014) have also modeled the effects of the trailing ocean cold wake using a different coupled model and found a similar effect.

The origin of the wake jet due to the modulation of the low-level flow over a long, narrow cold wake will be discussed here via Lagrangian trajectory analyses for the fully coupled EXPB experiments [see Fig. 59 in Chen (2014) for similar trajectories in the idealized wake-3 experiment]. Momentum budget analyses and air–sea flux calculations will then be examined following three selected trajectories to describe the physical mechanisms for the wake jet.

Deflections of air parcel trajectories due to the ocean cold wake in the EXPB experiment are analyzed for 10 trajectories released from the 10-m height at positions 60 km apart in 3-h intervals between 42 and 51 h and are tracked for 11 h. The three outer radii (about 480, 540, and 600 km behind the TC center) trajectories labeled as TJ8, TJ9, and TJ10 from the EXPB experiment that were released at 42 h are shown in Fig. 9a. The TJ8 and TJ9 trajectories are upstream of the cold wake and respond to the frictional convergence to ascend to 400–500 m. However, TJ10 (yellow line) first ascends before coming over the trailing end of the ocean wake, but then descends before passing out of the cold wake. By the 45-h release time at these same locations (Fig. 9b), the simulated trailing cold wake had expanded southward so that TJ8 and TJ9 also encountered the cold wake and descended. However, TJ10 had already ascended as a result of frictional convergence before reaching the cold-wake region. While both TJ8 and TJ9 were strongly deflected inward and crossed the cold-wake region, the path of the TJ8 was over the southern wake region and when TJ8 approached the leading edge it experienced weak ascent.

Fig. 9.
Fig. 9.

Zoomed-in view of three-dimensional (x, y, z) trajectories of the boundary layer airflow across the evolving SST distributions (shaded; contour interval: 0.5°C) at (a) 42, (b) 45, (c) 48, and (d) 51 h in the EXPB experiment in which the TC is moving at 2 m s−1 toward the southwest, which is from right to left. Three trajectories TJ8–TJ10 (see keys for colors) near the leading edge of the cold wake begin at 10-m height about 480, 540, and 600 km behind the TC center upwind from the cold wake at each starting time.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

The sensitivity of the location of the trajectory release positions relative to southward expanding cold wake is well illustrated in the 48-h plot (Fig. 9c). The TJ8 (blue line) is again strongly deflected inward across the cold wake all the way to the inner-core region where it has cyclonical rotation but does not ascend because TJ8 is still over relatively cold water. While the TJ9 (green line) is also deflected inward, its path is along the outer region of the cold wake. When TJ9 moves to the front of the cold-wake region, it ascends because of frictional convergence. Before the TJ10 (yellow line) reaches the cold wake it is ascending, but it then descends in the cold air above the wake while being deflected inward.

Finally, the three trajectories released just 3 h later (Fig. 9d) again illustrate the sensitivity to the positions relative to the southward expanding cold wake. The TJ8 (blue line) is again deflected inward completely across the cold wake to near the leading edge of the cold wake but now experiences cyclonic rotation in the inner core and TJ8 spirals upward. Although TJ9 (red line) is released just 60 km away from TJ8, its inward deflection brings it directly along the lowest SSTs in the cold wake and TJ9 remains at low levels. The TJ10 (yellow line) path is again deflected inward along the northern region of the cold wake and after a period of descent TJ10 rapidly ascends at the outer edge of the cold-wake region. However, TJ10 then rapidly descends and during the remaining hours of this 11-h trajectory the TJ10 alternately ascends and descends.

The TJ8 trajectories in Fig. 9 that are released from about 480 km behind the TC center at different times have some of the largest and most revealing interactions with the ocean cold wake. A summary of these interactions in terms of increased inflow angles of the low-level inflow and resulting ascent near the center of the TC is shown in Fig. 10. The TJ8 released at 42 h (blue line) has minimal interaction with the cold wake and thus reflects the typical inflow angle (Fig. 10a) and frictionally induced ascent (Fig. 10b). At 45 h, the TJ8 has only a brief ascent at the leading edge of the cold wake, and then the inflow angle is increased as TJ8 is deflected inward over the leading edge of the cold wake (Fig. 9b). Farther along this trajectory, the TJ8 air parcel is passing over the lowest SSTs in the cold wake, and then the large inward deflection (Fig. 10a) brings the air parcel into the inner core but near the leading edge of the cold wake so the ascent is about 80 m (Fig. 10b). The TJ8 release at 48 h starts over the leading edge of the cold wake but the inflow angle soon increases (Fig. 10a). Since the TJ8 has a path directly over the minimum SST and into the TC inner core over higher SSTs (Fig. 9c), the ascent (Fig. 10b) is limited by the lower air temperatures resulting from this long path over the cold wake. The TJ8 trajectory released at 51 h is similar to that released at 48 h with a large inflow angle (Fig. 10a) and with a path more across the cold wake. Consequently, the descending portion dominates and some small oscillations in height are simulated after about 8 h along this 11-h trajectory.

Fig. 10.
Fig. 10.

Plots of the trajectory TJ8 (a) inflow angle (°) and (b) ascent distance (m) during the same 11-h trajectories with release times as in Fig. 9 (see keys for line definitions).

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

The time variations of the atmospheric cold pool (ACP) above the cold ocean wake are also associated with the diurnal cycle as well as by outward-propagating rainbands. A larger and stronger ACP means a longer travel time required for air parcels such as TJ8 to climb over this atmospheric cold dome. Furthermore, there is also a distinct oscillation of rainbands on the diurnal time scale [see Figs. 60–63 in Chen (2014)]. Dunion et al. (2014) showed observational evidence of a TC diurnal pulse that begins near the storm center at sunset each day and propagates outward until the following late afternoon. The model-simulated rainbands, sensible heat flux over the wake, and the associated ACP have similar diurnal variations.

b. Momentum budget

In COAMPS, the changes of horizontal momentum are calculated in the Cartesian sigma coordinate as the sum of the local change, pressure gradient force, damping, horizontal advection, vertical advection, Coriolis, vertical mixing, and horizontal diffusion.

This horizontal momentum budget in COAMPS in Cartesian coordinate is output at the trajectory time and then is transformed to cylindrical coordinates centered on the model-simulated TC eye. Thus, the u and υ momentum tendency equations are transformed to the radial (υrad) and tangential (υT) momentum tendency equations.

As the air parcels cross the cold wake at outer radii well beyond the RMW in the two-way coupled trailing-cold-wake EXB experiment, the TC winds above the boundary layer are continually adjusting to achieve gradient wind balance
e1
where f is the Coriolis, υ is the wind speed, r is the distance to the center of the TC, ∂φ/∂r is the pressure gradient force, and φ is the geopotential. The Coriolis and centrifugal force terms on the left-hand side of Eq. (1) are balanced by the radial pressure-gradient force (RPFG) on the right-hand side. In the TC boundary layer, the acceleration of the radial wind is modulated by the flux divergence and the vertical and horizontal advection terms in additional to the Coriolis and RPGF. The gradient wind approximation implies that all three terms in Eq. (1) would have been adjusted as a result of the change of flux divergence across the cold wake and the resulting acceleration/deceleration of the radial wind.

To quantify the radial and tangential wind changes following the TJ8 released at 48 h and when TJ8 is crossing over the ocean cold wake toward lower SSTs (Fig. 11, middle), large oscillations in the tangential wind (Fig. 11b) and radial wind (Fig. 11a) tendencies are initiated in conjunction with the corresponding tangential and radial pressure gradient force terms (TPGF and RPGF, respectively). Negative RPGF indicates increased inflow toward the TC center. Between 48 and 51 h these total wind tendencies are mostly coincident with the TPGF and RPGF having an initial small inward motion leading to a large increase in TPGF and thus an acceleration in the tangential wind. While this increase in tangential wind increases the vertical mixing term, it also increases the Coriolis term in the radial wind equation that deflects the air parcel outward with a decrease in the RPGF. Between 48.5 and 50 h, the net effect of these oscillations is to slow the tangential wind and increase the inflow (negative υrad tendency).

Fig. 11.
Fig. 11.

(a) Radial wind and (b) tangential wind tendency budgets from two-way coupled EXPB experiment following trajectory TJ8 air parcel across the cold wake. (middle) The sea surface temperature along the trajectory is shown. The total wind component tendency (cyan) is the sum of tendencies from Coriolis (blue), horizontal advection (red), vertical advection (yellow), vertical mixing (purple), and pressure gradient (green).

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

After 50 h, the TJ8 is being deflected to lower SST values (Fig. 11, middle) and the radial wind tendencies begin to lead to changes in the RPGF that are offset in part by the horizontal advection term (Fig. 11a). Then an event occurs between 52 and 53 h in which large negative values of the RPGF lead to larger radial inflow because the horizontal advection only partially offsets the RPGF (Fig. 11a). After an adjustment period of about an hour, an even larger imbalance between the negative RPGF and the positive horizontal advection leads to a large inward (negative) radial wind tendency at 54.4 h. This time is when TJ8 is nearing the center of the cold wake with a SST of about 28.5°C.

A similar evolution between the TPGF and the tangential wind tendency (Fig. 11b) occurs after 51.5 h with first a phase lag of the TPGF as the horizontal advection term increases. Presumably because of the much larger tangential winds than radial winds, the tangential horizontal advection is larger than the TPGF for the event at 53 h and the tangential wind tendency is positive and large. However, this event leads to an opposite event at 54 h in which large negative TPGF and the tangential wind tendency are again coincident in time.

While the passage of TJ8 over the cold wake initiates large oscillations and imbalances in terms, the Coriolis term in the tangential wind equation (+) is generally increasing in time (Fig. 11b, blue line) throughout the period. That is, the radial wind component following the trajectory TJ8 is increasing in time as TJ8 moves over the cold wake. This radial wind is the wake jet that is advecting moisture inward toward the center in the range of 7–10RMV in Fig. 8b. For example, at 54-h forecast time the radial wind tendency at the 0.66-km level has an acceleration of the wake jet over the cold wake occurring approximately 200 km on the right side of the TC center and extends toward the eyewall (Fig. 12a). The increased radial inflow tendency at this location mainly stems from the RPGF (Fig. 12b) and the vertical mixing. However, the Coriolis term (Fig. 12c) and the sum of the residual terms (not shown) is acting to decrease the radial inflow tendency. Because the centrifugal force tendency is very small (not shown), the imbalance of the gradient wind tendency is driven by the Coriolis and RPGF. The location at which the acceleration of wake jet occurs is in an area where the stable TC boundary exist (Fig. 12d). The definition of the stable TC boundary layer here follows Lee and Chen (2014, see their section 3), except that the boundary layer height is diagnosed directly from the COAMPS turbulent PBL scheme. The 48–52-h axisymmetric composite of the radial wind profile indicates the mean increase of the wake-jet wind speed is ~1.8 m s−1 relative to a composite mean of ~9 m s−1. By contrast, the increase of the wake jet in the fixed wake-3 experiment is ~1.1 m s−1 from a composite mean of ~6 m s−1 (not shown).

Fig. 12.
Fig. 12.

TC-relative (a) radial wind tendency (m s−2), (b) tendency of radial pressure gradient force (RTGF; m s−2), (c) tendency of Coriolis (m s−2), and (d) the TC boundary layer stability (K m−1) for two-way coupled EXPB simulation at the 0.66-km level. The unstable and neutral stabilities are masked out in (d). The black contours are the sea surface temperature between 28°–30°C with a contour interval of 0.5°C. The black arrows denote the wind barbs at the 0.66-km level.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

In summary, this momentum balance in the two-way coupled EXPB experiment is generally consistent with the idealized wake-3 experiment in that the pressure gradient has the largest contribution to the radial wind speed increase. The advantage of the wake-3 experiment was that the fixed SST pattern amplified and localized the impacts of the cold wake. Compared to the idealized wake-3 experiment, the magnitude of the flux divergence term is smaller in the two-way coupled EXPB experiment because of the smaller SST gradient at the edge of the simulated cold wake. Nonlinear interactions and evolving SST anomalies in the EXPB experiment are considered to be more representative of the actual response of the tropical cyclone circulation as it passes over its cold wake.

5. Summary

Fixed and interactive (fully coupled) ocean-cold-wake experiments were compared to their control simulations to understand the TC response to the cold-wake magnitude and shape. Analyses of the TC thermodynamic and dynamic responses to the wakes were here based only on the azimuthal-mean composites with respect to the TC center. In agreement with prior studies, these experiments confirm that the wakes underneath the eyewall region are more efficient in spinning down the TC than a trailing wake. The key result from these experiments is the reduction of intensity in the long trailing-wake experiments was delayed by more than 12 h despite the areal coverage of the cold anomaly being roughly the same as for the fixed-wake experiments. A similar delay in the intensity reduction was also simulated in the interactive two-way coupled experiments that have a trailing wake.

The TC dynamic response from the cold-wake forcing is more complicated compared to a direct thermodynamic impact, which is an immediate response to the SST under the eyewall. In all of the wake experiments, the reduction in the surface fluxes following the imposition of the cold wake did not immediately reduce the surface wind speed. The further delayed response in intensity for the trailing-wake cases implies an enhanced transport of moist inflow air into the eyewall updrafts that tends to offset the negative effect of decreasing enthalpy flux from the ocean.

The two-way coupled experiments in general do agree with the fixed-wake experiments. A momentum budget following the air parcel trajectories in the fixed and interactive trailing-cold-wake experiments reveals the increased pressure gradient, vertical mixing, and Coriolis terms contributions to increased inflow over the wake. While the horizontal and vertical advection terms are also large over the wake, these terms tend to have opposite signs and the net contribution to the radial inflow tendency from these advection terms is small. In disagreement with the fixed trailing-cold-wake-3 experiment, the flux divergence term is smaller compared to these three other terms owing to a smaller SST gradient at the edge of the cold wake.

As the air parcels travel across the cold wake at outer radii well beyond the RMW in the two-way coupled trailing-cold-wake EXB experiment, the TC wind above the boundary layer is in gradient wind balance. The radial wind momentum budget analysis indicates that this balance is achieved through the change of pressure gradient, flux divergence, Coriolis, and the horizontal and vertical advection. In the two-way coupled simulation, the pressure gradient term has the largest contribution to the increase of radial wind speed tendency over the wake. As a result, an axisymmetric composite-mean 1–2 m s−1 increase of low- to midlevel inflow occurred above the cold wake (referred to as the “wake jet” owing to the location of the increased secondary circulation over the ocean cold wake) that is induced in response to an imbalance among these terms.

The main new findings presented in this study are summarized by the conceptual model (Fig. 13), which illustrates the physical processes governing the model-simulated TC interaction with its cold wake. First, these processes include complex dynamical pathway induced by the ocean cold wake that acts in concert with the enthalpy flux to modulate the TC intensity change. Second, the shape and location of the wake are relevant to the TC intensity change because they affect the time delay of the vortex spindown. A long trailing wake or irregularly shaped wake within the eyewall region forces a dynamic response that tends to offset the negative effect of reduced enthalpy flux and increase the time delay of the vortex spindown. Third, a 1–2 m s−1 increase of low- to midlevel inflow referred to as the “wake jet” occurs above an atmospheric cold pool, which is induced by the reverse sensible flux transfer over the trailing cold wake and augmented by net outgoing longwave fluxes during the night. As the low-level boundary level boundary inflow crosses the ocean wake, air parcels can be deflected upward but are turned toward the center of TC, which helps retain the moisture within and above the boundary layer.

Fig. 13.
Fig. 13.

Conceptual model of the physical processes affecting the atmospheric response in a TC moving from right to left while interacting with a trailing ocean cold wake (green color) with an atmospheric cold pool (light blue) above that cold wake. The gray shading depicts the locations of clouds, and the blue column represents the eye of the TC. The white arrows are the winds. The cooling underneath the eyewall forces an outward expansion of the eyewall. In addition to the thermodynamic processes related to a reduction in the enthalpy flux from the ocean to the TC boundary layer, a dynamic response of a low-level wake jet leads to inflow of moist air that delays or offsets the thermodynamic response to the cold wake.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

One important aspect of the TC interaction with its cold wake that has not been explored here is the influence of different atmosphere and ocean background state, such as the effects of the vertical wind shear, initial SST magnitude and gradient, and preexisting ocean eddies. The background state will modulate the TC interaction with its cold wake and the TC intensity delay time caused by its trailing cold wake. Future coupled model studies can extend the understanding of the modulation effects of the mean background state.

The model simulations presented here also suggest the need for additional observations over the cold wake to further elucidate and validate the structural changes in the TC dynamics and behavior described here. Current observation platforms may not properly characterize the TC boundary layer inflow changes across its cold wake due to rain contamination in scatterometer winds or lack of temporal and spatial resolution from in situ dropsonde observations across and along the cold wake. One suggestion is to include dropsondes with high temporal and spatial resolution both along the wake and across the wake. Such additional observations would supplement current observational strategies that have yet to address the implications of the wake-induced changes in the atmospheric circulations, and potentially on the ocean circulations as well. It is often the case that modeling results such as these lead to improved observing strategies that reveal important new aspects of the circulation that can further help isolate the underlying dynamics as well as improve coupled-model validation efforts. Thus, additional observational studies on the flow response over the cold ocean wake are needed to quantify the changes imposed by the ocean cold wake.

Acknowledgments

Dr. Jerome Schmidt’s assistance in providing the COAMPS turbulent and microphysics upgrades for this work is greatly appreciated. We thank Dr. Ren-Chieh Lien of the University of Washington for providing the ITOP mooring data. We appreciate the critical comments from three anonymous reviewers. Sue Chen was supported by the Naval Research Laboratory Award N0001415WX20094 and the Office of Naval Research Award N0001415WX00852 under Program Element PE062435N. Professor Russell Elsberry was supported by the Office of Naval Research Marine Meteorology section and Professor Patrick Harr was supported by the Naval Postgraduate School. The computing resources for the model simulations were provided by the Department of Defense High Performance Computing Modernization Program. Mrs. Penny Jones provided assistance in preparing the manuscript. A portion of this work was presented at the AMS 32nd Conference on Hurricanes and Tropical Meteorology.

APPENDIX

The initial atmospheric thermodynamic profile for all experiments is from the Gray et al. (1975) composite-mean nighttime tropical cloud-cluster sounding over the western North Pacific Ocean (Table A1 and Fig. A1). For the atmosphere–ocean two-way coupled experiment, the initial ocean temperature and salinity profiles are shown in Table A2 and Fig. A2.

Table A1.

Temperature, mixing ratio, and relative humidity values from the nighttime mean tropical cloud-cluster sounding of Gray et al. (1975).

Table A1.
Fig. A1.
Fig. A1.

Initial atmospheric temperature (solid) and dewpoint temperature (long dashed) profiles of mean nighttime tropical cloud-cluster soundings over the western North Pacific (Gray et al. 1975) for all experiments.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

Table A2.

Initial ocean temperature and salinity profile for the two-way coupled EXPA and EXPB experiments. The composite is derived from ITOP surface and subsurface moorings A1, A2, A4, SA1, SA2, and SA4 for pre-Fanapi during 14–16 Sep 2010.

Table A2.
Fig. A2.
Fig. A2.

Initial ocean temperature (black) and salinity (blue) profiles for the two-way coupled EXPA and EXPB experiments.

Citation: Journal of the Atmospheric Sciences 74, 12; 10.1175/JAS-D-16-0246.1

REFERENCES

  • Balaguru, K., P. Chang, R. Saravanan, L. R. Leung, Z. Xu, M. Li, and J. S. Hsieh, 2012: Ocean barrier layers’ effect on tropical cyclone intensification. Proc. Natl. Acad. Sci. USA, 109, 14 34314 347, doi:10.1073/pnas.1201364109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bender, M. A., and I. Ginis, 2000: Real-case simulations of hurricane–ocean interaction using a high-resolution coupled model: Effects on hurricane intensity. Mon. Wea. Rev., 128, 917946, doi:10.1175/1520-0493(2000)128<0917:RCSOHO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S. W., and R. A. Anthes, 1978: Numerical simulations of the ocean’s nonlinear, baroclinic response to translating hurricanes. J. Phys. Oceanogr., 8, 468480, doi:10.1175/1520-0485(1978)008<0468:NSOTON>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S. W., and R. A. Anthes, 1979: The mutual response of the tropical cyclone and the ocean. J. Phys. Oceanogr., 9, 128135, doi:10.1175/1520-0485(1979)009<0128:TMROTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S., 2014: Modeling interaction of a tropical cyclone with its cold wake. Ph.D. dissertation, Naval Postgraduate School, 248 pp.

  • Chen, S., T. J. Campbell, H. Jin, S. Gaberšek, R. M. Hodur, and P. J. Martin, 2010: Effect of two-way air-sea coupling in high and low wind speed regimes. Mon. Wea. Rev., 138, 35793602, doi:10.1175/2009MWR3119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cione, J. J., and E. W. Uhlhorn, 2003: Sea surface temperature variability in hurricanes: Implications with respect to intensity change. Mon. Wea. Rev., 131, 17831796, doi:10.1175//2562.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., T. B. Sanford, P. P. Niiler, and E. J. Terrill, 2007: Cold wake of Hurricane Frances. Geophys. Res. Lett., 34, L15609, doi:10.1029/2007GL030160.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., 2002: Coupled atmosphere–ocean wave simulations under high wind conditions. Mon. Wea. Rev., 130, 30873099, doi:10.1175/1520-0493(2002)130<3087:CAOWSU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Coauthors, 2012: Real-time tropical cyclone prediction using COAMPS-TC. Advances in Geophysics, Vol. 28, Academic Press, 15–28, doi:10.1142/9789814405683_0002.

    • Crossref
    • Export Citation
  • Dunion, J. P., and C. S. Marron, 2008: A reexamination of the Jordan mean tropical sounding based on awareness of the Saharan Air Layer: Results from 2002. J. Climate, 21, 52425253, doi:10.1175/2008JCLI1868.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dunion, J. P., C. D. Thorncroft, and C. S. Velden, 2014: The tropical cyclone diurnal cycle of mature hurricanes. Mon. Wea. Rev., 142, 39003919, doi:10.1175/MWR-D-13-00191.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, doi:10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frank, W. M., and E. A. Ritchie, 1999: Effects of environmental flow upon tropical cyclone structure. Mon. Wea. Rev., 127, 20442061, doi:10.1175/1520-0493(1999)127<2044:EOEFUT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, W. M., E. Ruprecht, and R. Phelps, 1975: Relative humidity in tropical weather systems. Mon. Wea. Rev., 103, 685690, doi:10.1175/1520-0493(1975)103<0685:RHITWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jacob, S. D., and L. K. Shay, 2003: The role of oceanic mesoscale features on the tropical cyclone-induced mixed layer response: A case study. J. Phys. Oceanogr., 33, 649676, doi:10.1175/1520-0485(2003)33<649:TROOMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jacob, S. D., and C. J. Koblinsky, 2007: Effects of precipitation on the upper-ocean response to a hurricane. Mon. Wea. Rev., 135, 22072225, doi:10.1175/MWR3366.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaimes, B., and L. K. Shay, 2009: Mixed layer cooling in mesoscale oceanic eddies during Hurricanes Katrina and Rita. Mon. Wea. Rev., 137, 41884207, doi:10.1175/2009MWR2849.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaimes, B., and L. K. Shay, 2010: Near-inertial wave wake of Hurricanes Katrina and Rita over mesoscale oceanic eddies. J. Phys. Oceanogr., 40, 13201337, doi:10.1175/2010JPO4309.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 1995: The evolution of vortices in vertical shear: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821851, doi:10.1002/qj.49712152406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 2000a: The evolution of vortices in vertical shear. II: Large scale asymmetries. Quart. J. Roy. Meteor. Soc., 126, 31373159, doi:10.1002/qj.49712657008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 2000b: The evolution of vortices in vertical shear. III: Baroclinic vortices. Quart. J. Roy. Meteor. Soc., 126, 31613185, doi:10.1002/qj.49712657009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jordan, C. L., 1958: Mean soundings for the West Indies area. J. Meteor., 15, 9197, doi:10.1175/1520-0469(1958)015<0091:MSFTWI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., and S. S. Chen, 2012: Symmetric and asymmetric structures of hurricane boundary layer in coupled atmosphere–wave–ocean models and observations. J. Atmos. Sci., 69, 35763594, doi:10.1175/JAS-D-12-046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., and S. S. Chen, 2014: Stable boundary layer and its impact on tropical cyclone structure in a coupled atmosphere–ocean model. Mon. Wea. Rev., 142, 19271944, doi:10.1175/MWR-D-13-00122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, I. I., C. C. Wu, I.-F. Pun, and D.-S. Ko, 2008: Upper-ocean thermal structure and the western North Pacific category 5 typhoons. Part I: Ocean features and the category 5 typhoons’ intensification. Mon. Wea. Rev., 136, 32883306, doi:10.1175/2008MWR2277.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, I. I., I. F. Pun, and C. C. Wu, 2009: Upper-ocean thermal structure and the western North Pacific category 5 typhoons. Part II: Dependence on translation speed. Mon. Wea. Rev., 137, 37443757, doi:10.1175/2009MWR2713.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, B., H. Liu, L. Xie, C. Guan, and D. Zhao, 2011: A coupled atmosphere–wave–ocean modeling system: Simulation of the intensity of an idealized tropical cyclone. Mon. Wea. Rev., 139, 132152, doi:10.1175/2010MWR3396.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, M., J. E. Nachamkin, and D. L. Westphal, 2009: On the improvement of COAMPS weather forecasts using an advanced radiative transfer model. Wea. Forecasting, 24, 286306, doi:10.1175/2008WAF2222137.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lynch, P., and X. Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 10191034, doi:10.1175/1520-0493(1992)120<1019:IOTHMU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ma, Z., J. Fei, L. Liu, X. Huang, and X. Cheng, 2013: Effects of the cold core eddy on tropical cyclone intensity and structure under idealized air–sea interaction conditions. Mon. Wea. Rev., 141, 12851303, doi:10.1175/MWR-D-12-00123.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mainelli-Huber, M., 2000: On the role of the upper ocean in tropical cyclone intensity change. M.S. thesis, Division of Meteorology and Physical Oceanography, RSMAS, University of Miami, Miami, FL, 73 pp.

  • Martin, P. J., 2000: Description of the Navy coastal ocean model version 1.0. Naval Research Laboratory Memo. Rep. NRL/FR/7322-00-9962, 45 pp.

  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806, doi:10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mrvaljevic, R. K., P. G. Black, L. R. Centurioni, Y.-T. Chang, E. A. D’Asaro, S. R. Jayne, and C. M. Lee, 2013: Observations of the cold wake of Typhoon Fanapi (2010). Geophys. Res. Lett., 40, 316321, doi:10.1029/2012GL054282.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279283, doi:10.1038/nature01481.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Price, J. F., 1981: Upper ocean response to a hurricane. J. Phys. Oceanogr., 11, 153175, doi:10.1175/1520-0485(1981)011<0153:UORTAH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Price, J. F., 2009: Metrics of hurricane-ocean interaction: Vertically-integrated or vertically-averaged ocean temperature? Ocean Sci., 5, 351368, doi:10.5194/os-5-351-2009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., S. Lorsolo, P. Reasor, J. Gamache, and F. Marks, 2012: Multiscale analysis of tropical cyclone kinematic structure from airborne Doppler radar composites. Mon. Wea. Rev., 140, 7799, doi:10.1175/MWR-D-10-05075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sanford, T. B., J. F. Price, and J. B. Girton, 2011: Upper-ocean response to Hurricane Frances (2004) observed by profiling EM-APEX floats. J. Phys. Oceanogr., 41, 10411056, doi:10.1175/2010JPO4313.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shay, L. K., 2010: Air-sea interactions in tropical cyclones. Global Perspectives on Tropical Cyclones: From Science to Mitigation, J. C. L. Chan and J. D. Kepert, Eds., World Scientific Series on Asia-Pacific Weather and Climate, Vol. 4, World Scientific Publishing, 93–132.

    • Crossref
    • Export Citation
  • Shay, L. K., P. G. Black, A. J. Mariano, J. D. Hawkins, and R. L. Elsberry, 1992: Upper ocean response to Hurricane Gilbert. J. Geophys. Res., 97, 20 22720 248, doi:10.1029/92JC01586.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, T. A., S. Chen, T. Campbell, E. Rogers, S. Gabersek, D. Wang, S. Carroll, and R. Allard, 2013: Ocean–wave coupled modeling in COAMPS-TC: A study of Hurricane Ivan (2004). Ocean Dyn., 69, 181194, doi:10.1016/j.ocemod.2013.06.003.

    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., L. Romero, J. C. McWilliams, and W. K. Melville, 2012: Transient evolution of Langmuir turbulence in ocean boundary layers driven by hurricane winds and waves. J. Phys. Oceanogr., 42, 19591980, doi:10.1175/JPO-D-12-025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vincent, E. M., M. Lengaigne, G. Madec, J. Vialard, G. Samson, N. C. Jourdain, C. E. Menkes, S. Jullien, 2012: Processes setting the characteristics of sea surface cooling induced by tropical cyclones. J. Phys. Oceanogr., 117, C02020, doi:10.1029/2011JC007396.

    • Search Google Scholar
    • Export Citation
  • Wong, M. L., and J. C. Chan, 2004: Tropical cyclone intensity in vertical wind shear. J. Atmos. Sci., 61, 18591876, doi:10.1175/1520-0469(2004)061<1859:TCIIVW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, C.-C., C.-Y. Lee, and I.-I. Lin, 2007: The effect of the ocean eddy on tropical cyclone intensity. J. Atmos. Sci., 64, 35623578, doi:10.1175/JAS4051.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhu, H., U. Wolfgang, and S. K. Roger, 2004: Ocean effects on tropical cyclone intensification and inner-core asymmetries. J. Atmos. Sci., 61, 12451258, doi:10.1175/1520-0469(2004)061<1245:OEOTCI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save
  • Balaguru, K., P. Chang, R. Saravanan, L. R. Leung, Z. Xu, M. Li, and J. S. Hsieh, 2012: Ocean barrier layers’ effect on tropical cyclone intensification. Proc. Natl. Acad. Sci. USA, 109, 14 34314 347, doi:10.1073/pnas.1201364109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bender, M. A., and I. Ginis, 2000: Real-case simulations of hurricane–ocean interaction using a high-resolution coupled model: Effects on hurricane intensity. Mon. Wea. Rev., 128, 917946, doi:10.1175/1520-0493(2000)128<0917:RCSOHO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S. W., and R. A. Anthes, 1978: Numerical simulations of the ocean’s nonlinear, baroclinic response to translating hurricanes. J. Phys. Oceanogr., 8, 468480, doi:10.1175/1520-0485(1978)008<0468:NSOTON>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S. W., and R. A. Anthes, 1979: The mutual response of the tropical cyclone and the ocean. J. Phys. Oceanogr., 9, 128135, doi:10.1175/1520-0485(1979)009<0128:TMROTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S., 2014: Modeling interaction of a tropical cyclone with its cold wake. Ph.D. dissertation, Naval Postgraduate School, 248 pp.

  • Chen, S., T. J. Campbell, H. Jin, S. Gaberšek, R. M. Hodur, and P. J. Martin, 2010: Effect of two-way air-sea coupling in high and low wind speed regimes. Mon. Wea. Rev., 138, 35793602, doi:10.1175/2009MWR3119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cione, J. J., and E. W. Uhlhorn, 2003: Sea surface temperature variability in hurricanes: Implications with respect to intensity change. Mon. Wea. Rev., 131, 17831796, doi:10.1175//2562.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., T. B. Sanford, P. P. Niiler, and E. J. Terrill, 2007: Cold wake of Hurricane Frances. Geophys. Res. Lett., 34, L15609, doi:10.1029/2007GL030160.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., 2002: Coupled atmosphere–ocean wave simulations under high wind conditions. Mon. Wea. Rev., 130, 30873099, doi:10.1175/1520-0493(2002)130<3087:CAOWSU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Coauthors, 2012: Real-time tropical cyclone prediction using COAMPS-TC. Advances in Geophysics, Vol. 28, Academic Press, 15–28, doi:10.1142/9789814405683_0002.

    • Crossref
    • Export Citation
  • Dunion, J. P., and C. S. Marron, 2008: A reexamination of the Jordan mean tropical sounding based on awareness of the Saharan Air Layer: Results from 2002. J. Climate, 21, 52425253, doi:10.1175/2008JCLI1868.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dunion, J. P., C. D. Thorncroft, and C. S. Velden, 2014: The tropical cyclone diurnal cycle of mature hurricanes. Mon. Wea. Rev., 142, 39003919, doi:10.1175/MWR-D-13-00191.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, doi:10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frank, W. M., and E. A. Ritchie, 1999: Effects of environmental flow upon tropical cyclone structure. Mon. Wea. Rev., 127, 20442061, doi:10.1175/1520-0493(1999)127<2044:EOEFUT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, W. M., E. Ruprecht, and R. Phelps, 1975: Relative humidity in tropical weather systems. Mon. Wea. Rev., 103, 685690, doi:10.1175/1520-0493(1975)103<0685:RHITWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jacob, S. D., and L. K. Shay, 2003: The role of oceanic mesoscale features on the tropical cyclone-induced mixed layer response: A case study. J. Phys. Oceanogr., 33, 649676, doi:10.1175/1520-0485(2003)33<649:TROOMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jacob, S. D., and C. J. Koblinsky, 2007: Effects of precipitation on the upper-ocean response to a hurricane. Mon. Wea. Rev., 135, 22072225, doi:10.1175/MWR3366.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaimes, B., and L. K. Shay, 2009: Mixed layer cooling in mesoscale oceanic eddies during Hurricanes Katrina and Rita. Mon. Wea. Rev., 137, 41884207, doi:10.1175/2009MWR2849.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jaimes, B., and L. K. Shay, 2010: Near-inertial wave wake of Hurricanes Katrina and Rita over mesoscale oceanic eddies. J. Phys. Oceanogr., 40, 13201337, doi:10.1175/2010JPO4309.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 1995: The evolution of vortices in vertical shear: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821851, doi:10.1002/qj.49712152406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 2000a: The evolution of vortices in vertical shear. II: Large scale asymmetries. Quart. J. Roy. Meteor. Soc., 126, 31373159, doi:10.1002/qj.49712657008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 2000b: The evolution of vortices in vertical shear. III: Baroclinic vortices. Quart. J. Roy. Meteor. Soc., 126, 31613185, doi:10.1002/qj.49712657009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jordan, C. L., 1958: Mean soundings for the West Indies area. J. Meteor., 15, 9197, doi:10.1175/1520-0469(1958)015<0091:MSFTWI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., and S. S. Chen, 2012: Symmetric and asymmetric structures of hurricane boundary layer in coupled atmosphere–wave–ocean models and observations. J. Atmos. Sci., 69, 35763594, doi:10.1175/JAS-D-12-046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., and S. S. Chen, 2014: Stable boundary layer and its impact on tropical cyclone structure in a coupled atmosphere–ocean model. Mon. Wea. Rev., 142, 19271944, doi:10.1175/MWR-D-13-00122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, I. I., C. C. Wu, I.-F. Pun, and D.-S. Ko, 2008: Upper-ocean thermal structure and the western North Pacific category 5 typhoons. Part I: Ocean features and the category 5 typhoons’ intensification. Mon. Wea. Rev., 136, 32883306, doi:10.1175/2008MWR2277.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, I. I., I. F. Pun, and C. C. Wu, 2009: Upper-ocean thermal structure and the western North Pacific category 5 typhoons. Part II: Dependence on translation speed. Mon. Wea. Rev., 137, 37443757, doi:10.1175/2009MWR2713.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, B., H. Liu, L. Xie, C. Guan, and D. Zhao, 2011: A coupled atmosphere–wave–ocean modeling system: Simulation of the intensity of an idealized tropical cyclone. Mon. Wea. Rev., 139, 132152, doi:10.1175/2010MWR3396.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, M., J. E. Nachamkin, and D. L. Westphal, 2009: On the improvement of COAMPS weather forecasts using an advanced radiative transfer model. Wea. Forecasting, 24, 286306, doi:10.1175/2008WAF2222137.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lynch, P., and X. Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 10191034, doi:10.1175/1520-0493(1992)120<1019:IOTHMU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ma, Z., J. Fei, L. Liu, X. Huang, and X. Cheng, 2013: Effects of the cold core eddy on tropical cyclone intensity and structure under idealized air–sea interaction conditions. Mon. Wea. Rev., 141, 12851303, doi:10.1175/MWR-D-12-00123.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mainelli-Huber, M., 2000: On the role of the upper ocean in tropical cyclone intensity change. M.S. thesis, Division of Meteorology and Physical Oceanography, RSMAS, University of Miami, Miami, FL, 73 pp.

  • Martin, P. J., 2000: Description of the Navy coastal ocean model version 1.0. Naval Research Laboratory Memo. Rep. NRL/FR/7322-00-9962, 45 pp.

  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806, doi:10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mrvaljevic, R. K., P. G. Black, L. R. Centurioni, Y.-T. Chang, E. A. D’Asaro, S. R. Jayne, and C. M. Lee, 2013: Observations of the cold wake of Typhoon Fanapi (2010). Geophys. Res. Lett., 40, 316321, doi:10.1029/2012GL054282.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279283, doi:10.1038/nature01481.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Price, J. F., 1981: Upper ocean response to a hurricane. J. Phys. Oceanogr., 11, 153175, doi:10.1175/1520-0485(1981)011<0153:UORTAH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Price, J. F., 2009: Metrics of hurricane-ocean interaction: Vertically-integrated or vertically-averaged ocean temperature? Ocean Sci., 5, 351368, doi:10.5194/os-5-351-2009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., S. Lorsolo, P. Reasor, J. Gamache, and F. Marks, 2012: Multiscale analysis of tropical cyclone kinematic structure from airborne Doppler radar composites. Mon. Wea. Rev., 140, 7799, doi:10.1175/MWR-D-10-05075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sanford, T. B., J. F. Price, and J. B. Girton, 2011: Upper-ocean response to Hurricane Frances (2004) observed by profiling EM-APEX floats. J. Phys. Oceanogr., 41, 10411056, doi:10.1175/2010JPO4313.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shay, L. K., 2010: Air-sea interactions in tropical cyclones. Global Perspectives on Tropical Cyclones: From Science to Mitigation, J. C. L. Chan and J. D. Kepert, Eds., World Scientific Series on Asia-Pacific Weather and Climate, Vol. 4, World Scientific Publishing, 93–132.

    • Crossref
    • Export Citation
  • Shay, L. K., P. G. Black, A. J. Mariano, J. D. Hawkins, and R. L. Elsberry, 1992: Upper ocean response to Hurricane Gilbert. J. Geophys. Res., 97, 20 22720 248, doi:10.1029/92JC01586.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, T. A., S. Chen, T. Campbell, E. Rogers, S. Gabersek, D. Wang, S. Carroll, and R. Allard, 2013: Ocean–wave coupled modeling in COAMPS-TC: A study of Hurricane Ivan (2004). Ocean Dyn., 69, 181194, doi:10.1016/j.ocemod.2013.06.003.

    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., L. Romero, J. C. McWilliams, and W. K. Melville, 2012: Transient evolution of Langmuir turbulence in ocean boundary layers driven by hurricane winds and waves. J. Phys. Oceanogr., 42, 19591980, doi:10.1175/JPO-D-12-025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vincent, E. M., M. Lengaigne, G. Madec, J. Vialard, G. Samson, N. C. Jourdain, C. E. Menkes, S. Jullien, 2012: Processes setting the characteristics of sea surface cooling induced by tropical cyclones. J. Phys. Oceanogr., 117, C02020, doi:10.1029/2011JC007396.

    • Search Google Scholar
    • Export Citation
  • Wong, M. L., and J. C. Chan, 2004: Tropical cyclone intensity in vertical wind shear. J. Atmos. Sci., 61, 18591876, doi:10.1175/1520-0469(2004)061<1859:TCIIVW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, C.-C., C.-Y. Lee, and I.-I. Lin, 2007: The effect of the ocean eddy on tropical cyclone intensity. J. Atmos. Sci., 64, 35623578, doi:10.1175/JAS4051.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhu, H., U. Wolfgang, and S. K. Roger, 2004: Ocean effects on tropical cyclone intensification and inner-core asymmetries. J. Atmos. Sci., 61, 12451258, doi:10.1175/1520-0469(2004)061<1245:OEOTCI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Schematic illustration of the ocean-cold-wake-1–wake-3 sensitivity experiments: (a) a circle-shape wake 1 (2) with a 2° (4°)C cold anomaly centered under the TC at x = 250 km, y = 250 km and (b) an oval-shape wake 3 that is 270 km in length and is located to the right rear of the TC center that is at the same position as in wakes 1 and 2. The yellow circle depicts the uncoupled CNTL radius of maximum wind.

  • Fig. 2.

    Comparison of the (a) maximum wind speeds (m s−1) and (b) minimum sea level pressures (hPa) between the CNTL and the wake-1–3 experiments, in which the coupling begins instantaneously at hour 36. See the keys for the line definitions for the wake experiments.

  • Fig. 3.

    Total enthalpy flux (104 W m−2) within the RMW (cyan bar) and within 200-km radius (blue bar) at 42–54 h for the CNTL and wake-1–3 experiments. The white and blue numbers above each cyan and blue bars are their corresponding total enthalpy flux (104 W m−2).

  • Fig. 4.

    Composites of the azimuthal-mean tangential wind speed (contour interval: 5 m s−1) at 42–54 h from (a) CNTL, (b) wake-1, (c) wake-2, and (d) wake-3 experiments. Black line represents the RMW at each level.

  • Fig. 5.

    As in Fig. 4, but for the azimuthal-mean radial wind components (contour interval: 2 m s−1). The maximum low-level radial inflow wind speeds for CNTL, wake 1, wake 2, and wake 3 are 15, 8.8, 8.3, and 12 m s−1 respectively. (e) A zoomed-in view of (d) in the lowest 2 km.

  • Fig. 6.

    Composites of the azimuthal-mean radial pressure gradients (hPa km−1) from (a) CNTL, (b) wake-1, (c) wake-2, and (d) wake-3 experiments at 42–54 h.

  • Fig. 7.

    Sea surface temperature anomalies (°C; color scale on the right) and 10-m wind stress (m2 s−2; red contours, interval: 0.001 m2 s−2) near the model-simulated TC at 42 h from simulations (a) EXPA with a 0 m s−1 westward translation speed and (b) EXPB with a 2 m s−1 westward translation speed. The 10-m wind stress (red) and current (black) vectors are plotted every two grid points.

  • Fig. 8.

    (a) Composite radial wind speed (m s−1; interval: 1 m s−1, negative values denote inflow) and (b) mixing ratio (kg kg−1; interval: 0.5 × 10−4 kg kg−1) anomalies at 42–54 h for the EXPB relative to the unc EXPB. Black dotted line represents the RMW at each level scaled by the RMW (16.5 km) at the 10-m height level.

  • Fig. 9.

    Zoomed-in view of three-dimensional (x, y, z) trajectories of the boundary layer airflow across the evolving SST distributions (shaded; contour interval: 0.5°C) at (a) 42, (b) 45, (c) 48, and (d) 51 h in the EXPB experiment in which the TC is moving at 2 m s−1 toward the southwest, which is from right to left. Three trajectories TJ8–TJ10 (see keys for colors) near the leading edge of the cold wake begin at 10-m height about 480, 540, and 600 km behind the TC center upwind from the cold wake at each starting time.

  • Fig. 10.

    Plots of the trajectory TJ8 (a) inflow angle (°) and (b) ascent distance (m) during the same 11-h trajectories with release times as in Fig. 9 (see keys for line definitions).

  • Fig. 11.

    (a) Radial wind and (b) tangential wind tendency budgets from two-way coupled EXPB experiment following trajectory TJ8 air parcel across the cold wake. (middle) The sea surface temperature along the trajectory is shown. The total wind component tendency (cyan) is the sum of tendencies from Coriolis (blue), horizontal advection (red), vertical advection (yellow), vertical mixing (purple), and pressure gradient (green).

  • Fig. 12.

    TC-relative (a) radial wind tendency (m s−2), (b) tendency of radial pressure gradient force (RTGF; m s−2), (c) tendency of Coriolis (m s−2), and (d) the TC boundary layer stability (K m−1) for two-way coupled EXPB simulation at the 0.66-km level. The unstable and neutral stabilities are masked out in (d). The black contours are the sea surface temperature between 28°–30°C with a contour interval of 0.5°C. The black arrows denote the wind barbs at the 0.66-km level.

  • Fig. 13.

    Conceptual model of the physical processes affecting the atmospheric response in a TC moving from right to left while interacting with a trailing ocean cold wake (green color) with an atmospheric cold pool (light blue) above that cold wake. The gray shading depicts the locations of clouds, and the blue column represents the eye of the TC. The white arrows are the winds. The cooling underneath the eyewall forces an outward expansion of the eyewall. In addition to the thermodynamic processes related to a reduction in the enthalpy flux from the ocean to the TC boundary layer, a dynamic response of a low-level wake jet leads to inflow of moist air that delays or offsets the thermodynamic response to the cold wake.

  • Fig. A1.

    Initial atmospheric temperature (solid) and dewpoint temperature (long dashed) profiles of mean nighttime tropical cloud-cluster soundings over the western North Pacific (Gray et al. 1975) for all experiments.

  • Fig. A2.

    Initial ocean temperature (black) and salinity (blue) profiles for the two-way coupled EXPA and EXPB experiments.