1. Introduction
The generation and intensification processes of tropical cyclones (TCs) have been investigated for decades. Observations have revealed that strong TCs often experience a rapidly intensifying period after an initial slow development (e.g., Sitkowski and Barnes 2009). In their statistical study, Kaplan and DeMaria (2003) defined a rapid intensification (RI) phase as the rate of change in maximum sustained wind speed being equal to or greater than 15.4 m s−1 (24 h)−1. They showed that all Atlantic basin hurricanes that are either category 4 or 5 undergo an RI phase at least once during their lifetimes. Therefore, the intensification phase of such strong TCs can be divided into two different phases in terms of the rate of intensification. This infers that such TCs mainly intensify through at least two mechanisms during the whole period of TC intensification.
The mechanisms for the intensification as well as the steady-state maintenance of TCs have been studied from observational, analytical, and numerical points of view. Emanuel (1986, 1989) proposed an air–sea interaction theory on TC intensification by assuming moist slantwise neutrality in the eyewall, so-called the wind-induced surface heat exchange (WISHE) theory. This theory describes that the intensification process is spontaneous as follows: given a cyclonic disturbance on the warm ocean, winds at the ocean surface drive sea surface enthalpy fluxes and the increased enthalpy fluxes, whose magnitude approximately depends linearly on the wind speed, enhance the radial gradient of equivalent potential temperature θe in the upper troposphere, which in turn accelerates the tangential wind in the lowest layer of the atmosphere [see Fig. 1 of Montgomery et al. (2009)]. Such a spontaneous intensification is one of the fastest intensifying processes that a TC experiences during its lifetime and therefore is referred to as RI in this study.
However, during an initial intensification before the RI, the vorticity of TCs is originally provided from both large-scale tropical disturbances (e.g., Ritchie and Holland 1999) and mesoscale convective disturbances (e.g., Bister and Emanuel 1997; Ritchie and Holland 1997). Recent studies have pointed out the importance of convective-scale processes, such as vortical hot towers (VHTs), that are characterized by strong convection with a significant cyclonic vorticity (Hendricks et al. 2004), especially during the early stage of TC intensification. Montgomery et al. (2006) conducted a numerical experiment to show that the simulated TC-scale vortex is generated from a mesoscale convective vortex–like disturbance and intensifies through the merger of numerous VHTs. The VHTs are strengthened by stretching of the vertical vorticity through convective updrafts. Once VHTs are generated on the cyclonic disturbance, the VHTs move to the core region where the vorticity of background circulation is large. In general, positive (negative) vortices move up the background gradient of positive (negative) vorticity (Schecter and Dubin 1999, 2001). Therefore, convectively generated VHTs merge with each other around the core region. Van Sang et al. (2008) examined the TC intensification by conducting numerical simulations of a three-dimensional nonhydrostatic model and showed that the mergers of VHT-like vortices gradually enhance the low-level circulation with the increase in the size of each convective cell. From the analysis of satellite data for Tropical Storm Gert (2005), Braun et al. (2010) examined the intensifying mechanism for the vortex merger and emphasized the importance of VHTs for the intensification of the tropical storm.
As vorticity increases through the merger of VHTs and/or mesoscale convective systems (Ritchie and Holland 1997; Simpson et al. 1997), a TC goes into its RI phase. This phase change can be recognized as an increase in the rate of intensification (e.g., Sitkowski and Barnes 2009; Barnes and Fuentes 2010). Although the initial intensification and the RI seem to be relatively well understood, the transition process of TCs to the RI phase is not clear.
Rogers (2010) carried out a numerical simulation of Hurricane Dennis (2005) and examined the convective processes before and after the onset of RI of the simulated TC. It was found that the RI is triggered by the enhanced low-level convergence (i.e., secondary circulation). In addition, Rogers suggested that the inertial stability of a TC vortex should be a suitable factor for predicting whether a TC goes into its RI phase, because the large inertial stability in the core region results effectively in condensation heating for accelerating primary circulation (Schubert and Hack 1982; Shapiro and Willoughby 1982; Nolan et al. 2007). The importance of the inertial stability for the structural evolution of TCs is suggested by the theoretical study of Vigh and Schubert (2009). Based on analytical solutions of a balanced, frictionless fluid system (Sawyer–Eliassen equation), they found that high inertial stability plays an important role in rapidly intensifying a warm core. Guimond et al. (2010) examined the airborne Doppler radar and satellite observations of Hurricane Dennis (2005) and showed that during the initial development of Dennis (2005), convective downdrafts increase the temperature in the eye and the inward motions toward the eye. Barnes and Fuentes (2010) examined the observational data obtained from integrated aircraft reconnaissance and suggested that an eye excess energy, defined as the vertically integrated difference in θe between the eye and eyewall, can diagnose well the onset of RI. Once the eye excess energy is accumulated enough, the energy is released in the eyewall region; this condition is favorable for RI. In other words, the increase in θe in the eye is necessary for the transition to the RI phase.
Although prior studies suggest that the thermodynamic and kinematic properties of the TC core play an important role in initiating RI, it is still not clear how and when the TC vortex changes its phase to the RI. Therefore, the purpose of this study is to examine a mechanism for the transition of TCs to the RI phase. One control and two sensitivity experiments under idealized conditions are conducted with the use of a three-dimensional, nonhydrostatic numerical model. The model settings are described in section 2. In section 3, the results of the experiments are shown. Based on the numerical results, a mechanism for the transition to RI is proposed in section 4. We conclude this study in section 5.
2. Numerical model and experimental design
The Advanced Research Weather Research and Forecasting Model (ARW-WRF, version 3.0; Skamarock et al. 2008) is used to simulate the development of a TC. The WRF solves a fully compressible, nonhydrostatic equation set using the third-order Runge–Kutta time-integration scheme (Wicker and Skamarock 2002) and the fifth-order upwind-biased scheme for advection terms. The prognostic equations are for momentum in three dimensions—perturbation geopotential, perturbation potential temperature, perturbation surface pressure of dry air, and the mixing ratios of water contents [see details in Skamarock et al. (2008)].
Our approach to determine the experimental setups for the present numerical simulations is to set the model physics and atmospheric conditions as simple as possible in order to focus on the dynamics of TCs. With this thinking, a Kessler (1969)-type scheme is used for cloud microphysics, and the effects of radiation are not included. The subgrid turbulence is represented by the eddy viscosity calculated using stress tensor and length scale (Smagorinsky 1963; Lilly 1962). The surface exchange coefficients for momentum and enthalpy, which are critical parameters for the TC intensity during the intensification as well as the steady state (Emanuel 1995, 1997; Gray and Craig 1998; Montgomery et al. 2010; Wang and Xu 2010; Xu and Wang 2010; Miyamoto and Takemi 2010; Ito et al. 2011), are formulated based on recent experimental and observational studies (Donelan et al. 2004; Zhang et al. 2008).
The initial state of the model atmosphere is a horizontally homogeneous, resting atmosphere whose vertical profiles of temperature and water vapor mixing ratio are determined by a tropical mean sounding of Jordan (1958). An axisymmetric vortex formulated by Rotunno and Emanuel (1987) with the maximum wind speed of 12 m s−1 at the radius of 80 km is inserted at the center of the computational domain at the initial time. The experiment is carried out using a vortex-following two-way nesting method on an f plane with the constant f value of 5 × 10−5 s−1. The outer numerical domain covers a 3000 km × 3000 km area with 6-km horizontal grid spacing, while the inner domain covers a 600 km × 600 km area at 2-km resolution. Both domains use 44 vertical levels stretched with height up to the 50-hPa level. In the upper part of the domain, a damping layer of the 2846-m depth is applied to minimize unwanted gravity waves reflecting at the upper boundary. No orthogonal fluxes are permitted at the lateral and top boundaries. The bottom boundary is assumed to be sea surface whose temperature is fixed uniformly at 300 K during the integration. Under these experimental settings, the governing equations are integrated numerically for 200 h, with model output saved every hour except for the period from t = 75 to 120 h, during which the output is saved every 10 min. Analyses are performed primarily for this control experiment.
To confirm that the simulated results from the control experiment do not depend on the model parameterization and/or the initial condition, we carry out two experiments that investigate sensitivities to the cloud-microphysics parameterization and to the initial environment. The first experiment is done by changing the microphysics parameterization to a scheme including ice-phase processes (Goddard microphysics; Tao et al. 1989). The second experiment uses a mean tropical sounding obtained during the observational campaign in 2008 by the research vessel (R/V) Mirai of the Japan Agency for Marine-Earth Science and Technology (JAMSTEC; Geng et al. 2011). Note that the experimental settings are identical to the control experiment except for the microphysics or the initial sounding.
3. Results
The results of the control experiment are described in sections 3a–c. In section 3d, the results of the sensitivity experiments are examined to show the robustness of the numerical results of the control experiment.
a. Intensification and evolution of the simulated vortex
1) Definition of intensification phase
To diagnose the TC intensity, the maximum horizontal wind speed at the 1-km height is used in this study. Figure 1a shows the time series of the maximum wind speed and the radius of maximum horizontal wind rm. The maximum wind speed of the simulated TC starts increasing from t = 70 h and achieves the maximum around t = 150 h, while rm decreases from t = 70 h and becomes nearly constant after t = 113 h. After the intensification finishes (t = 150 h), the simulated TC reaches a quasi-steady state at which both the maximum wind speed and rm remain almost constant.
Time series of (a) maximum wind speed at the 1-km height υm (black solid line) and its radius rm (gray line) of the simulated TC vortex and (b) the rate of intensification. The intensification phase of the simulated TC is divided into three subphases in terms of the rate of intensification. The periods of these subphases are separated by thin dashed lines. See details in the main text.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) maximum wind speed at the 1-km height υm (black solid line) and its radius rm (gray line) of the simulated TC vortex and (b) the rate of intensification. The intensification phase of the simulated TC is divided into three subphases in terms of the rate of intensification. The periods of these subphases are separated by thin dashed lines. See details in the main text.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) maximum wind speed at the 1-km height υm (black solid line) and its radius rm (gray line) of the simulated TC vortex and (b) the rate of intensification. The intensification phase of the simulated TC is divided into three subphases in terms of the rate of intensification. The periods of these subphases are separated by thin dashed lines. See details in the main text.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Figure 1b shows the time series of the rate of change in the maximum wind speed, a proxy for the rate of intensification of the simulated TC. The intensification rate fluctuates around the zero value from t = 20 to 70 h and linearly increases after t = 70 h. Then, the rate sharply increases from t = 105 h and reaches the maximum value of 3.38 m s−1 h−1 at t = 113 h. Since the rate of the intensification rate between t = 105 h and 113 h rapidly increases with time, this period can be regarded as a spontaneous intensification phase, that is, an RI phase. After t = 113 h, the intensification rate sharply drops until t = 122 h and gradually decreases. Subsequent to t = 150 h, the rate varies around the zero value. Therefore, the intensification of the simulated TC occurs during the period from t = 70 to 150 h. We define this period as an intensification phase. According to the difference in the rate of the intensification rate, this phase is further divided into three subphases: 1) a slowly intensifying phase between t = 70 and 105 h, 2) an RI phase in which the rate of intensification sharply increases from t = 105 to 113 h, and 3) an adjustment phase toward the maximum intensity from t = 113 h to the end of intensification (t = 150 h). Since the definition of RI in this study is the spontaneous intensification during which a TC enhances the intensification rate by itself, the RI phase is defined here as the period when the intensification rate is large and increases with time.
Since the purpose of this study is to examine a transition mechanism for the RI, we mainly focus on the physical processes prior to phase 2 (i.e., a later period of phase 1). The processes in phase 3 are not discussed in the current paper.
2) Intensifying processes
To investigate transition processes to the RI, the evolution of the simulated TC structure is at first examined. Figures 2 depicts the spatial distributions of the vertically averaged Ertel’s potential vorticity (PV) at t = 85, 95, 105, and 115 h. The averages are indicated by the bar in this paper and hence the vertically averaged PV is written as 
Horizontal distributions of 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Horizontal distributions of
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Horizontal distributions of
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
To demonstrate physical processes before and during the RI (phase 2), temporal evolutions of thermodynamic variables are examined here. Since the overall evolution of TCs can be clearly indicated by θe in the upper troposphere, temporal evolutions of θe at the 12-km height at three different radii are diagnosed (Fig. 3a). The θe values shown in Fig. 3a are the areal average 
Time series of thermodynamic variables. (a) The black solid, gray thick, and black dashed lines show 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of thermodynamic variables. (a) The black solid, gray thick, and black dashed lines show
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of thermodynamic variables. (a) The black solid, gray thick, and black dashed lines show
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The time series of the surface enthalpy flux and the vertically averaged θe in the lowest 1 km at rm 
b. Axisymmetric and asymmetric evolution of the TC
The results described in section 3a showed that the horizontal distribution of 
1) Definition of axisymmetricity
The axisymmetricity using PV (γPV) averaged within the 100-km radius and between z = 1.5 and 12.0 km (i.e., 
Figure 4a shows the time series of 
(a) Time series of maximum wind speed (black solid line) and the axisymmetricity (gray solid line) defined by Eq. (2), which is averaged inside the 100-km radius and between 1.5 and 12 km vertically. The dashed vertical lines are identical to those in Fig. 1. The dash–dotted vertical gray line denotes t = 93 h, at which 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
(a) Time series of maximum wind speed (black solid line) and the axisymmetricity (gray solid line) defined by Eq. (2), which is averaged inside the 100-km radius and between 1.5 and 12 km vertically. The dashed vertical lines are identical to those in Fig. 1. The dash–dotted vertical gray line denotes t = 93 h, at which
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
(a) Time series of maximum wind speed (black solid line) and the axisymmetricity (gray solid line) defined by Eq. (2), which is averaged inside the 100-km radius and between 1.5 and 12 km vertically. The dashed vertical lines are identical to those in Fig. 1. The dash–dotted vertical gray line denotes t = 93 h, at which
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The axisymmetricities for other variables related to TC intensity—that is, kinetic energy γKE, tangential velocity γυ, and vertical velocity γw—are also calculated (Fig. 4b). The values are also averaged both in the radial and the vertical directions as in Fig. 2. When kinetic energy or tangential velocity is used as φ in Eq. (2), the increase in axisymmetricity (i.e., 
2) Energetic viewpoint of TC evolution
To understand how the axisymmetric and asymmetric processes contribute to the intensification of the simulated TC, we examine the processes before and after the RI starts (t = 105 h) from an energetic point of view by carrying out an energy budget analysis based on Kwon and Frank (2008).
Figure 5 shows the time series of KE and PE integrated in the volume within the 100-km radius and from the surface to the 16-km height. It should be noted that the scales of the vertical axes for the variables in the two panels of Fig. 5 are different. According to the decomposition defined in Eq. (1), KE and PE are divided into axisymmetric components that correspond to zero wavenumber component (WN = 0) and asymmetric ones (WN > 0). The axisymmetric part of kinetic energy density (KEWN=0) starts increasing after t = 30 h, and the rate of change is enhanced at t = 93 h. KEWN=0 achieves the maximum value at around t = 165 h. In contrast, the axisymmetric part of available potential energy density (PEWN=0) continuously increases throughout the integration. The increasing rate of PEWN=0 saturates at around t = 80 h and constantly increases during the rest of the simulation time.
Time series of (a) KE and (b) PE integrated over the analysis domain, which is inside the radius of 100 km and below the 16-km height. The WN 0 (axisymmetric) components are shown by the thick dark gray lines, while the components whose WN are higher than 0 and 5 are shown by the medium and light gray lines, respectively. Note that the scales of the vertical axes are different in the two figures. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) KE and (b) PE integrated over the analysis domain, which is inside the radius of 100 km and below the 16-km height. The WN 0 (axisymmetric) components are shown by the thick dark gray lines, while the components whose WN are higher than 0 and 5 are shown by the medium and light gray lines, respectively. Note that the scales of the vertical axes are different in the two figures. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) KE and (b) PE integrated over the analysis domain, which is inside the radius of 100 km and below the 16-km height. The WN 0 (axisymmetric) components are shown by the thick dark gray lines, while the components whose WN are higher than 0 and 5 are shown by the medium and light gray lines, respectively. Note that the scales of the vertical axes are different in the two figures. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The asymmetric components of both kinetic energy density and available potential energy density (KEWN>0 and PEWN>0) are further separated into higher wavenumber components (WN > 5) and the total asymmetric ones (WN > 0). Figure 5 shows that the asymmetric components (i.e., WN > 5 and WN > 0) of both KE and PE increase at least until t = 93 h. Subsequently, KEWN>0 decreases sharply until t = 113 h and then remains approximately constant until the end of the intensification (t = 150 h), whereas PEWN>0 steadily increases until the end of the intensification phase.
The differences of both KE and PE between the higher (WN > 5) and the total (WN > 0) asymmetric components are generally small, indicating that the effects of the low-wavenumber components (1 ≤ WN ≤ 5) are small. In other words, low-wavenumber motions such as vortex Rossby waves (e.g., Guinn and Schubert 1993; Montgomery and Kallenbach 1997) have little impact on the intensification during the period and thus high-wavenumber components that are considered to include convective-scale processes play a role in maintaining the asymmetric motion. Figure 6 shows the time series of the ratio of KEWN>0 to KEWN=0 within the volume defined above. The ratio before t = 93 h is larger than that after t = 93 h. This temporal change in the ratio indicates that the contribution of convective-scale processes should be significant in the TC core (within the 100-km radius) up to t = 93 h. After t = 93 h when the rate of change in KEWN=0 suddenly increases, the contributions of asymmetric components gradually become smaller than those of the axisymmetric components. This is consistent with the results that the simulated TC becomes well axisymmetric at t = 93 h as diagnosed by γPV (Fig. 4a).
Time series of the ratio of KEWN>0 to KEWN=0. The dash–dotted and dashed lines represent the time when the TC vortex becomes axisymmetric (t = 93 h) and when the RI commences (t = 105 h), respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the ratio of KEWN>0 to KEWN=0. The dash–dotted and dashed lines represent the time when the TC vortex becomes axisymmetric (t = 93 h) and when the RI commences (t = 105 h), respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the ratio of KEWN>0 to KEWN=0. The dash–dotted and dashed lines represent the time when the TC vortex becomes axisymmetric (t = 93 h) and when the RI commences (t = 105 h), respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The result that the high-wavenumber component of KE is dominant compared to the low-wavenumber component seems to be inconsistent with the results of Wang (2008) in his idealized numerical simulation. His results indicate that the low-wavenumber component of KE is significant in the core region, while the high-wavenumber component mainly presents only outside the TC core (see his Fig. 14). However, in the current experiment, it is also shown that the distributions of both high- and low-wavenumber components in a radius–time cross section are qualitatively similar to those of Wang (2008) (figures not shown). Since the components of KEWN>0 and KEWN>5 in the present experiment (Fig. 5) are evaluated in the volume including both the core and parts of the outer region, the high-wavenumber component, which is more dominant in the outer radii but less dominant in the core region, becomes more significant than the low-wavenumber one.
Figure 7 shows the time series of the budgets of Eq. (5). The energy conversion term between PE and KE in Eq. (5) is always positive, which means that PE is baroclinically converted to KE. This term generally increases throughout the three phases. However, after t = 93 h the barotropic energy conversion of KE between the WN = 0 and the WN > 0 components is mostly negative, indicating that KEWN=0 is converted to KEWN>0. The magnitude of the advection terms is significantly smaller than that of the other terms.
Time series of each term in conservation equations for KEWN=0 [Eq. (5)]. The energy conversion term between PE and KE is shown by the black line, while the conversion term between the components whose WN is 0 and WN higher than 0 is shown by the gray line. The advection term is shown by the light gray dashed line. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of each term in conservation equations for KEWN=0 [Eq. (5)]. The energy conversion term between PE and KE is shown by the black line, while the conversion term between the components whose WN is 0 and WN higher than 0 is shown by the gray line. The advection term is shown by the light gray dashed line. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of each term in conservation equations for KEWN=0 [Eq. (5)]. The energy conversion term between PE and KE is shown by the black line, while the conversion term between the components whose WN is 0 and WN higher than 0 is shown by the gray line. The advection term is shown by the light gray dashed line. The thin vertical lines are identical to those in Fig. 4.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The budgets of Eq. (7) and the asymmetric heating term (DHWN>0) in Eq. (8) are shown in Fig. 8. Prior to t = 93 h, both the axisymmetric and asymmetric components of the energy source due to the diabatic heating are equally present (Fig. 8b). After t = 93 h (Fig. 4), the axisymmetric heating (DHWN=0) significantly increases, which continues during phase 2. This is consistent with the results diagnosed by the axisymmetricity [Eq. (2)]. After t = 120 h, the increase in the heating rate becomes smaller until the heating approaches the maximum value. This temporal change in DHWN=0 seems to be well correlated with that of the energy conversion term between KE and PE. In contrast, DHWN>0 no longer increases after t = 93 h. Corresponding to the decrease in DHWN>0, the energy conversion of PE from the WN = 0 to the WN > 0 component is small. As in the budgets of KE, the contribution of the advection terms is negligible.
As in Fig. 7, but for (a) budgets of the conservation equations for PEWN=0 [Eq. (7)] and (b) the time series of DH terms in both axisymmetric and asymmetric equations [Eqs. (7) and (8)]. (b) The thick and thin lines denote the axisymmetric and asymmetric components, respectively. The source terms of PE due to the DH of WN 0 (axisymmetric) and WN higher than 0 (asymmetric) components are shown by the black solid and thin lines, respectively. Note that the scale in the vertical axis is approximately one order larger than that of Fig. 7.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 7, but for (a) budgets of the conservation equations for PEWN=0 [Eq. (7)] and (b) the time series of DH terms in both axisymmetric and asymmetric equations [Eqs. (7) and (8)]. (b) The thick and thin lines denote the axisymmetric and asymmetric components, respectively. The source terms of PE due to the DH of WN 0 (axisymmetric) and WN higher than 0 (asymmetric) components are shown by the black solid and thin lines, respectively. Note that the scale in the vertical axis is approximately one order larger than that of Fig. 7.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 7, but for (a) budgets of the conservation equations for PEWN=0 [Eq. (7)] and (b) the time series of DH terms in both axisymmetric and asymmetric equations [Eqs. (7) and (8)]. (b) The thick and thin lines denote the axisymmetric and asymmetric components, respectively. The source terms of PE due to the DH of WN 0 (axisymmetric) and WN higher than 0 (asymmetric) components are shown by the black solid and thin lines, respectively. Note that the scale in the vertical axis is approximately one order larger than that of Fig. 7.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The intensification phase of the simulated TC from the energy budget analysis is summarized as follows. As the TC vortex becomes nearly axisymmetric (Fig. 4), the axisymmetric component of diabatic heating increases (Fig. 8b). The heating enhances PEWN=0, which is in turn converted to the axisymmetric component of KE (Figs. 7 and 8a). As a result, KEWN=0 increases and then the simulated TC intensifies.
It was also shown in the analyses of the axisymmetricity and the energy budget that the simulated TC vortex becomes axisymmetric at t = 93 h, which is 12 h before the onset of RI. In the observational study of Sitkowski and Barnes (2009), the inner-core region of Hurricane Guillermo (1997) clearly indicated a circular-shaped structure during the RI. The structure of the simulated TC core is consistent with this observed feature.
c. Dynamic and thermodynamic properties around the onset of RI
From the previous results, it was indicated that the simulated TC goes into the RI phase at t = 105 h, which is 12 h after the TC becomes axisymmetric. In this subsection, the dynamic and thermodynamic properties before and after the RI starts are focused on in order to demonstrate the processes of the transition to the RI phase.
Figure 9 depicts the horizontal distributions of 
As in Fig. 2, but for t = (a) 97, (b) 100, (c) 103, and (d) 106 h, and with the vertically averaged water content (shaded, interval = 0.5 g kg−1). The interval of 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 2, but for t = (a) 97, (b) 100, (c) 103, and (d) 106 h, and with the vertically averaged water content (shaded, interval = 0.5 g kg−1). The interval of
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 2, but for t = (a) 97, (b) 100, (c) 103, and (d) 106 h, and with the vertically averaged water content (shaded, interval = 0.5 g kg−1). The interval of
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Figure 10 exhibits the horizontal distributions of vertical velocity 
As in Fig. 9, but for the vertical velocity (shaded) and the potential temperature deviation from the horizontal average (contoured). The counter interval for 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 9, but for the vertical velocity (shaded) and the potential temperature deviation from the horizontal average (contoured). The counter interval for
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 9, but for the vertical velocity (shaded) and the potential temperature deviation from the horizontal average (contoured). The counter interval for
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Figure 11 depicts the radius–height sections of the tangentially averaged diabatic heating rate 
Radius–height sections of the heating rate due to the diabatic process (shaded), the radial velocity (black contour), and the angular momentum (gray contour) at t = (a) 97, (b) 100, (c) 103, and (d) 106 h. The variables are tangentially averaged. The positive (negative) values are indicated by the solid (dashed) contours. The color interval is 10 K h−1, and the maximum is 70 K h−1. The intervals of the radial velocity and the angular momentum are 0.5 m s−1 and 5 × 105 m2 s−1, respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Radius–height sections of the heating rate due to the diabatic process (shaded), the radial velocity (black contour), and the angular momentum (gray contour) at t = (a) 97, (b) 100, (c) 103, and (d) 106 h. The variables are tangentially averaged. The positive (negative) values are indicated by the solid (dashed) contours. The color interval is 10 K h−1, and the maximum is 70 K h−1. The intervals of the radial velocity and the angular momentum are 0.5 m s−1 and 5 × 105 m2 s−1, respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Radius–height sections of the heating rate due to the diabatic process (shaded), the radial velocity (black contour), and the angular momentum (gray contour) at t = (a) 97, (b) 100, (c) 103, and (d) 106 h. The variables are tangentially averaged. The positive (negative) values are indicated by the solid (dashed) contours. The color interval is 10 K h−1, and the maximum is 70 K h−1. The intervals of the radial velocity and the angular momentum are 0.5 m s−1 and 5 × 105 m2 s−1, respectively.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As time passes, the contours of 
As Rogers (2010) and Guimond et al. (2010) stated, the enhancement of low-level convergence is a triggering mechanism for RI of Hurricane Dennis (2005). As shown in Fig. 11, the enhancement of convergence of low-level inflow is linked to the intensification of updrafts. Figures 10 and 11 show that the strong upward motion confined in the TC core is closely related to the initiation of RI. Hence, temporal changes in the intensity and location of vertical mass fluxes are examined. The time series of the local and azimuthally averaged maximum vertical mass fluxes at z = 12.5 km (Fm and 
Time series of the vertical mass fluxes of (a) the local maximum (light gray line) and the azimuthally averaged maximum (dark gray line) and (b) those radii (light gray line and dark gray line) with the radius of maximum azimuthally averaged horizontal wind at the 1-km height; rma is shown by the black line. The fluxes are calculated at the 12.5-km height. The vertical lines stand for the period of RI.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the vertical mass fluxes of (a) the local maximum (light gray line) and the azimuthally averaged maximum (dark gray line) and (b) those radii (light gray line and dark gray line) with the radius of maximum azimuthally averaged horizontal wind at the 1-km height; rma is shown by the black line. The fluxes are calculated at the 12.5-km height. The vertical lines stand for the period of RI.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the vertical mass fluxes of (a) the local maximum (light gray line) and the azimuthally averaged maximum (dark gray line) and (b) those radii (light gray line and dark gray line) with the radius of maximum azimuthally averaged horizontal wind at the 1-km height; rma is shown by the black line. The fluxes are calculated at the 12.5-km height. The vertical lines stand for the period of RI.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
The vertical mass flux is well correlated with the diabatic heating after the onset of RI as shown in Figs. 9–11, and so is the confinement of 
To demonstrate the transition phase from the establishment of axisymmetricity (t = 93 h) to the initiation of RI (t = 105 h), the thermodynamic aspects of the simulated TC are examined here. Figure 13 indicates the temporal and radial changes of convective available potential energy (CAPE), rma, θe averaged in the lowest 500-m layer 
Time–radius cross section of the 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time–radius cross section of the
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time–radius cross section of the
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
d. Sensitivity experiments
In this subsection, the sensitivities of the results of the current idealized experiment, especially the enhancement of CAPE within rma, to the physics parameterization and initial condition are examined and the results of the sensitivity experiments are briefly shown. Figures 14a and 14b depict the time–radius cross sections of 
As in Fig. 13, but for (a) the experiment with the microphysics parameterization–solving ice-phase processes (Goddard microphysics scheme) and (b) the experiment with the initial sounding obtained in the observational campaign in 2008 by JAMSTEC.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 13, but for (a) the experiment with the microphysics parameterization–solving ice-phase processes (Goddard microphysics scheme) and (b) the experiment with the initial sounding obtained in the observational campaign in 2008 by JAMSTEC.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
As in Fig. 13, but for (a) the experiment with the microphysics parameterization–solving ice-phase processes (Goddard microphysics scheme) and (b) the experiment with the initial sounding obtained in the observational campaign in 2008 by JAMSTEC.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
4. A proposed mechanism for the transition to RI
a. Linkage between CAPE accumulation and axisymmetricity
Based on the results obtained in section 3, a transition mechanism to the RI is investigated in this section. In Fig. 13, it was shown that CAPE rapidly increases after the TC core becomes axisymmetric and the high CAPE condition continues until RI starts, suggesting that the axisymmetrization is a key factor in increasing the CAPE value. Furthermore, from a dynamical aspect, the axisymmetrization will increase the inertial stability of the TC core. Therefore, we hypothesize that the rapid increase in CAPE within rma is closely related to the enhancement of inertial stability.
Time series of the equivalent potential temperature (black dashed line), inertial stability (black solid line) defined by Eq. (9), and 
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the equivalent potential temperature (black dashed line), inertial stability (black solid line) defined by Eq. (9), and
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of the equivalent potential temperature (black dashed line), inertial stability (black solid line) defined by Eq. (9), and
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
It is noteworthy that 
As a next step, a Lagrangian trajectory analysis for air parcels originating in the core region is carried out in order to examine the relationship between I2 and air motion within the core region. The movements of the air parcels are calculated by the two-step method of Doty and Perkey (1993). First, 81 parcels are seeded at the grid points at the lowest model layer (z = 30.0 m) within the radius of 20 km at a given time. Then, the trajectories of the parcels are calculated by the simulated wind field at every 10 min until the parcels pass over either the 30-km radius, which approximately corresponds to the outer edge of the high CAPE region (Fig. 13), or the 500-m height below, which the thermodynamic variables are vertically averaged for the calculation of CAPE. The wind outputs at 10-min intervals are linearly interpolated at 1-min resolution. From given position and time, the location of a parcel as a first guess is calculated with the use of the horizontally and vertically interpolated winds at the given time step and then winds at the point after the displacement are obtained by interpolating three-dimensional wind data at the next time step. The winds at the two different locations at two consecutive times are averaged and used to determine the movement of the parcel after a single time step (Takemi and Satomura 2000).
Figure 16a shows the time series of the eye residence time, which represents how long the seeded parcels stay within a control volume inside the 30-km radius and below the 500-m height. Note that the residence time is estimated by the averages for the 81 parcels. It is shown that at t = 93 h, the residence time sharply increases from about 1 to 2–3.5 h and becomes shorter than 2 h after t = 105 h. Figure 16b shows the time series of whether the parcels pass through the control volume at the lateral or the top boundary. If all parcels pass through the lateral boundary, then the value is plotted at “lateral 100%” in the vertical axes. Before t = 93 h all the parcels pass at the lateral boundary, whereas subsequent to t = 93 h, the percentage of the parcels that pass through the top boundary becomes significant. After t = 99 h, few parcels pass through the lateral boundary.
Time series of (a) the residence time that is the period from the seeding time to when parcels pass through either the outer edge or the top of the control volume and (b) the boundaries at which the parcels pass. The vertical axis in (b) represents that if all parcels pass through the top (lateral) boundary, the line is drawn at “vertical 100%” (“lateral 100%”). The dashed and dash–dotted lines are identical to those in Fig. 15.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) the residence time that is the period from the seeding time to when parcels pass through either the outer edge or the top of the control volume and (b) the boundaries at which the parcels pass. The vertical axis in (b) represents that if all parcels pass through the top (lateral) boundary, the line is drawn at “vertical 100%” (“lateral 100%”). The dashed and dash–dotted lines are identical to those in Fig. 15.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Time series of (a) the residence time that is the period from the seeding time to when parcels pass through either the outer edge or the top of the control volume and (b) the boundaries at which the parcels pass. The vertical axis in (b) represents that if all parcels pass through the top (lateral) boundary, the line is drawn at “vertical 100%” (“lateral 100%”). The dashed and dash–dotted lines are identical to those in Fig. 15.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
b. Discussion: A proposed mechanism for the transition to RI
The increase in surface enthalpy flux as well as the residence time occurs possibly due to the axisymmetrization of the simulated TC (Fig. 4a). Since the enhanced secondary circulation results in strong vertical velocity below the 500-m height and the increased I2 prevent parcels from passing through the lateral boundary, parcels tend to move upward rather than outward. Inside rma, the vertical motion is an order of magnitude weaker than the horizontal motion (figure not shown). As a result, parcels can stay longer within rma after the TC becomes nearly axisymmetric.
Since the trajectory analysis suggests that the residence time is closely related to I2, the relationship between the residence time and the enthalpy that an air parcel (along a trajectory) obtains from the underlying ocean is estimated and shown in Fig. 17. Note that the enthalpy is an integrated value during the period when an air parcel is located at the lowest level (i.e., when a parcel is at 15 ≤ z ≤ 52 m). It is obvious that the enthalpy obtained through the sea surface fluxes before t = 93 h (black circles) is smaller than after t = 93 h (dark gray rectangles and light gray circles). Once the TC is axisymmetric (i.e., t = 93 h), the residence time substantially becomes long and the accumulated enthalpy in turn enhances. After the onset of RI (after t = 105 h), the obtained enthalpy is still large (light gray circles), although the residence time becomes shorter. This seems to result from the enhanced secondary circulation.
Relationship between the residence time and the enthalpy that a trajectory obtains from the underlying ocean during its passage. Both quantities are the averaged values using all trajectories initialized every 10 min. The sea surface enthalpy flux is integrated during the period when a trajectory is located at the lowest model level. The black circles, gray squares, and light gray circles stand for the relationships estimated from t = 75 to 93 h, from t = 93 to 105 h, and from t = 105 to 120 h, respectively. Note that the results in which the residence time exceeds the calculation period (3 h) are removed from this figure.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Relationship between the residence time and the enthalpy that a trajectory obtains from the underlying ocean during its passage. Both quantities are the averaged values using all trajectories initialized every 10 min. The sea surface enthalpy flux is integrated during the period when a trajectory is located at the lowest model level. The black circles, gray squares, and light gray circles stand for the relationships estimated from t = 75 to 93 h, from t = 93 to 105 h, and from t = 105 to 120 h, respectively. Note that the results in which the residence time exceeds the calculation period (3 h) are removed from this figure.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
Relationship between the residence time and the enthalpy that a trajectory obtains from the underlying ocean during its passage. Both quantities are the averaged values using all trajectories initialized every 10 min. The sea surface enthalpy flux is integrated during the period when a trajectory is located at the lowest model level. The black circles, gray squares, and light gray circles stand for the relationships estimated from t = 75 to 93 h, from t = 93 to 105 h, and from t = 105 to 120 h, respectively. Note that the results in which the residence time exceeds the calculation period (3 h) are removed from this figure.
Citation: Journal of the Atmospheric Sciences 70, 1; 10.1175/JAS-D-11-0285.1
It is confirmed that parcels obtain more enthalpy from the ocean as the residence time becomes longer. As a result, θe and hence CAPE increase inside rma after t = 93 h. Once CAPE becomes sufficiently large for continuous convective activity, the TC becomes ready for the formation of the eyewall.
In contrast, the axisymmetrized structure of the TC vortex enhances the axisymmetric component of diabatic heating as well as the secondary circulation. It is shown that as I2 increases, the diabatic heating around the eyewall region effectively works to enhance the TC intensity and the warm core rapidly develops. These processes are consistent with previous studies (e.g., Schubert and Hack 1982; Shapiro and Willoughby 1982; Nolan 2007; Vigh and Schubert 2009). Therefore, the axisymmetrized vortex accelerates the spinup process. Consequently, the axisymmetrization prior to the RI is necessary for both dynamic and thermodynamic evolutions of TCs.
5. Conclusions
To examine the mechanism for the transition of TCs to the RI phase, numerical experiments are carried out by using a three-dimensional, fully compressible numerical model (WRF). The intensification phase of the simulated TC is divided into three subphases according to the rate of the intensification: 1) a slowly intensifying phase (t = 70–105 h), 2) an RI phase (t = 105–113 h), and 3) an adjustment phase toward the quasi-steady state (t = 113–150 h). Specific analysis focusing on the intensification phase, including the RI phase of the simulated TC, reveals the following points. The WISHE mechanism seems to play a role in RI (phase 2) of the simulated TC (Fig. 3). In contrast, the energy budget analysis shows that PE generated by the axisymmetric diabatic heating is converted to the axisymmetric component of KE, which corresponds to the rotational motion of TC. The contribution of PE to the asymmetric component of KE is small compared to that of the axisymmetric one (Figs. 5–8). Since the intensifying process corresponds to the forming process of a single, vigorous peak of the vertically averaged PV at the center of circulation, a parameter, axisymmetricity γ [Eq. (2)] is defined in order to diagnose the degree to which the vortex is axisymmetric. Using γ, it is found that 12 h before the onset of RI, the simulated TC vortex becomes axisymmetric (Fig. 4). Axisymmetrization of the simulated TC vortex makes the TC core inertially stable. Both θe in the lowest 500 m and CAPE increase—especially inside rma—after the TC becomes nearly axisymmetric (Fig. 13). Subsequent to the onset of RI, the enhanced CAPE suddenly decreases and the convective activity is confined to the eyewall region (Figs. 9–13). In addition, the vertical mass flux is confined to r ≈ rma and becomes significant before the onset of RI (Fig. 12).
The Lagrangian trajectory analysis shows that axisymmetrization of the simulated TC enables air parcels to stay longer within the core region and to obtain a larger amount of enthalpy from the underlying ocean (Figs. 16 and 17). Intensifying surface wind speeds enhance sea surface fluxes and hence provide much enthalpy. Consequently, θe and CAPE increase within rma, where the eyewall subsequently forms and the maximum value of CAPE achieves 3500 J kg−1 (Fig. 13). The sudden increase in the vertical mass fluxes in the core region (or evolution of the secondary circulation) results in forming the eyewall by using the enhanced CAPE. The RI processes of the simulated TC are driven by the formation of the eyewall.
Given a cyclonic disturbance strong enough to obtain energy from the ocean, the transition mechanism to the RI phase of TCs proposed in this study is summarized below. The new findings of this study are items 1, 3, and 4:
A TC vortex becomes axisymmetric or at least starts axisymmetrization processes sufficiently before the start of RI.
As the TC vortex becomes axisymmetric, its I2 increases substantially and the axisymmetric component of diabatic heating effectively accelerates the primary and secondary circulations.
The large I2 increases the residence time of fluid parcels in the TC core, which results in the enhancement of boundary layer θe and hence CAPE within the rma.
An eyewall forms by utilizing the enhanced CAPE in the core region and then the RI processes are driven.
Acknowledgments
We would like to express our gratitude to Prof. H. Ishikawa, who provided a lot of fruitful discussion. We also thank Profs. C.-C. Wu and S. Yoden, Drs. G. H. Bryan and K. Ito, and Mr. R. Yoshida for giving us valuable suggestions. The comments by anonymous reviewers are greatly acknowledged for improving the original manuscript. This work is partly supported by JSPS Scientific Research Grant 20-776 for JSPS Research Fellows.
REFERENCES
Barnes, G. M., and P. Fuentes, 2010: Eye excess energy and the rapid intensification of Hurricane Lili (2002). Mon. Wea. Rev., 138, 1446–1458.
Bister, M., and K. A. Emanuel, 1997: The genesis of Hurricane Guillermo: TEXMEX analyses and a modeling study. Mon. Wea. Rev., 125, 2662–2682.
Braun, S. A., 2002: A cloud-resolving simulation of Hurricane Bob (1991): Storm structure and eyewall buoyancy. Mon. Wea. Rev., 130, 1573–1592.
Braun, S. A., M. T. Montgomery, K. J. Mallen, and P. D. Reasor, 2010: Simulation and interpretation of the genesis of Tropical Storm Gert (2005) as part of the NASA Tropical Cloud Systems and Processes Experiment. J. Atmos. Sci., 67, 999–1025.
Donelan, M. A., B. K. Haus, N. Reul, W. J. Plant, M. Stiassnie, H. C. Graber, O. B. Brown, and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett.,31, L18306, doi:10.1029/2004GL019460.
Doty, K. G., and D. J. Perkey, 1993: Sensitivity of trajectory calculations to the temporal frequency of wind data. Mon. Wea. Rev., 121, 387–401.
Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585–604.
Emanuel, K. A., 1989: The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46, 3431–3456.
Emanuel, K. A., 1995: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci., 52, 3969–3976.
Emanuel, K. A., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 1014–1026.
Geng, B., K. Yoneyama, R. Shirooka, and M. Yoshizaki, 2011: Characteristics of precipitation systems and their environment observed during the onset of the western North Pacific summer monsoon in 2008. J. Meteor. Soc. Japan, 89, 1–25.
Gray, S., and G. C. Craig, 1998: A simple theoretical model for the intensification of tropical cyclones and polar lows. Quart. J. Roy. Meteor. Soc., 124, 919–947.
Guimond, S. R., G. M. Heymsfield, and F. J. Turk, 2010: Multiscale observations of Hurricane Dennis (2005): The effects of hot towers on rapid intensification. J. Atmos. Sci., 67, 633–654.
Guinn, T. A., and W. H. Schubert, 1993: Hurricane spiral bands. J. Atmos. Sci., 50, 3380–3403.
Hendricks, E. A., M. T. Montgomery, and C. A. Davis, 2004: The role of vortical hot towers in the formation of Tropical Cyclone Diana (1984). J. Atmos. Sci., 61, 1209–1232.
Ito, K., Y. Ishikawa, Y. Miyamoto, and T. Awaji, 2011: Short-time-scale processes in a mature hurricane as a response to sea surface fluctuations. J. Atmos. Sci., 68, 2250–2272.
Jordan, C. L., 1958: Mean soundings for the West Indies area. J. Meteor., 15, 91–97.
Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18, 1093–1108.
Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulations.Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.
Kwon, Y. C., and W. M. Frank, 2008: Dynamic instabilities of simulated hurricane-like vortices and their impacts on the core structure of hurricanes. Part II: Moist experiments. J. Atmos. Sci., 65, 106–122.
Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, 14, 148–172.
Miyamoto, Y., and T. Takemi, 2010: An effective radius of the sea surface enthalpy flux for the maintenance of a tropical cyclone. Atmos. Sci. Lett., 11, 278–282.
Montgomery, M. T., and R. J. Kallenbach, 1997: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., 123, 435–465.
Montgomery, M. T., M. E. Nicholls, T. A. Cram, and A. B. Saunders, 2006: A vortical hot tower route to tropical cyclogenesis. J. Atmos. Sci., 63, 355–386.
Montgomery, M. T., S. Nguyen, and R. K. Smith, 2009: Do tropical cyclones intensify by WISHE? Quart. J. Roy. Meteor. Soc., 135, 1697–1714.
Montgomery, M. T., R. K. Smith, and S. Nguyen, 2010: Sensitivity of tropical-cyclone models to the surface drag coefficient. Quart. J. Roy. Meteor. Soc., 136, 1945–1953.
Nolan, D. S., 2007: What is the trigger for tropical cyclogenesis? Aust. Meteor. Mag., 56, 241–266.
Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64, 3377–3405.
Ritchie, E., and G. J. Holland, 1997: Scale interactions during the formation of typhoon Irving. Mon. Wea. Rev., 125, 1377–1396.
Ritchie, E., and G. J. Holland, 1999: Large-scale patterns associated with tropical cyclogenesis in the western Pacific. Mon. Wea. Rev., 127, 2027–2043.
Rogers, R., 2010: Convective-scale structure and evolution during a high-resolution simulation of tropical cyclone rapid intensification. J. Atmos. Sci., 67, 44–70.
Rotunno, R., and K. A. Emanuel, 1987: An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44, 542–561.
Schecter, D. A., and D. H. E. Dubin, 1999: Vortex motion driven by a background vorticity gradient. Phys. Rev. Lett., 83, 2191–2194.
Schecter, D. A., and D. H. E. Dubin, 2001: Theory and simulations of vortex motion driven by a background vorticity gradient. Phys. Fluids, 13, 1704–1723.
Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 1687–1697.
Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378–394.
Simpson, J., E. Ritchie, G. J. Holland, J. Halverson, and S. Stewart, 1997: Mesoscale interactions in tropical cyclone genesis. Mon. Wea. Rev., 125, 2643–2661.
Sitkowski, M., and G. M. Barnes, 2009: Low-level thermodynamic, kinematic, and reflectivity fields of Hurricane Guillermo (1997) during rapid intensification. Mon. Wea. Rev., 137, 645–663.
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang, and J. G. Powers, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp.
Smagorinsky, J., 1963: General circulation experiments with the primitive equations. I: The basic experiment. Mon. Wea. Rev., 91, 99–164.
Takemi, T., and T. Satomura, 2000: Numerical experiments on the mechanisms for the development and maintenance of long-lived squall lines in dry environments. J. Atmos. Sci., 57, 1718–1740.
Tao, W.-K., J. Simpson, and M. McCumber, 1989: An ice-water saturation adjustment. Mon. Wea. Rev., 117, 231–235.
Van Sang, N., R. K. Smith, and M. T. Montgomery, 2008: Tropical-cyclone intensification and predictability in three dimensions. Quart. J. Roy. Meteor. Soc., 134, 563–582.
Vigh, J. L., and W. H. Schubert, 2009: Rapid development of the tropical cyclone warm core. J. Atmos. Sci., 66, 3335–3350.
Wang, Y., 2008: Rapid filamentation zone in a numerically simulated tropical cyclone. J. Atmos. Sci., 65, 1158–1181.
Wang, Y., and J. Xu, 2010: Energy production, frictional dissipation, and maximum intensity of a numerically simulated tropical cyclone. J. Atmos. Sci., 67, 97–116.
Wicker, L. J., and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088–2097.
Xu, J., and Y. Wang, 2010: Sensitivity of tropical cyclone inner-core size and intensity to the radial distribution of surface entropy flux. J. Atmos. Sci., 67, 1831–1852.
Zhang, J. A., P. G. Black, J. R. French, and W. M. Drennan, 2008: First direct measurements of enthalpy flux in the hurricane boundary layer: The CBLAST results. Geophys. Res. Lett.,35, L14813, doi:10.1029/2008GL034374.
