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Isaac Ginis
and
Georgi Sutyrin

Abstract

A theory of the depth-averaged currents and sea surface elevation generated by a moving hurricane in a stratified ocean with flat bottom is presented. Using a scale analysis of the depth-integrated momentum and continuity equations, it is found that the depth-averaged currents are nearly nondivergent and determined entirely by the wind stress curl. Earth's rotation and ocean stratification have negligible effects. The sea surface elevation is decomposed into four physically different parts caused by geostrophic adjustment to the depth-averaged currents, wind stress divergence, inverted barometer offset, and baroclinic effects. When a hurricane moves with a uniform speed, it generates quasi-stationary, alongtrack, elongated depth-averaged currents. The sea surface elevation remaining after the hurricane passage is a combination of a trough geostrophically adjusted with the depth-averaged currents and a sea surface elevation associated with baroclinic effects.

The barotropic response is analysed for different wind stress distribution. A universal nondimensional description of the depth-averaged flow is suggested, using scaling based on the maximum wind stress torque LTL and its radius L. This marks the primary difference with baroclinic responses where the radius of maximum winds, Rm , and maximum wind stress Tm are the determining scales. For all cases considered, the maximum depth-averaged current is proportional to LTL and the distance from the maximum to the storm track is proportional to L. The wind stress behavior at the hurricane's periphery is shown to be an important feature in .determining the sea surface response.

Analytical solutions of approximated equations agree well with numerical simulations based on the full set of equations. It is demonstrated, using a two-layer model, that nonlinear coupling between the baroclinic and barotropic modes is rather weak, and therefore they may be calculated separately.

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Yalin Fan
,
Isaac Ginis
, and
Tetsu Hara

Abstract

In coupled ocean–atmosphere models, it is usually assumed that the momentum flux into ocean currents is equal to the flux from air (wind stress). However, when the surface wave field grows (decays) in space or time, it gains (loses) momentum and reduces (increases) the momentum flux into subsurface currents compared to the flux from the wind. In particular, under tropical cyclone (TC) conditions the surface wave field is complex and fast varying in space and time and may significantly affect the momentum flux from wind into ocean. In this paper, numerical experiments are performed to investigate the momentum flux budget across the air–sea interface under both uniform and idealized TC winds. The wave fields are simulated using the WAVEWATCH III model. The difference between the momentum flux from wind and the flux into currents is estimated using an air–sea momentum flux budget model. In many of the experiments, the momentum flux into currents is significantly reduced relative to the flux from the wind. The percentage of this reduction depends on the choice of the drag coefficient parameterization and can be as large as 25%. For the TC cases, the reduction is mainly in the right-rear quadrant of the hurricane, and the percentage of the flux reduction is insensitive to the changes of the storm size and the asymmetry in the wind field but varies with the TC translation speed and the storm intensity. The results of this study suggest that it is important to explicitly resolve the effect of surface waves for accurate estimations of the momentum flux into currents under TCs.

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Yalin Fan
,
Isaac Ginis
, and
Tetsu Hara

Abstract

In this paper, the wind–wave–current interaction mechanisms in tropical cyclones and their effect on the surface wave and ocean responses are investigated through a set of numerical experiments. The key element of the authors’ modeling approach is the air–sea interface model, which consists of a wave boundary layer model and an air–sea momentum flux budget model. The results show that the time and spatial variations in the surface wave field, as well as the wave–current interaction, significantly reduce momentum flux into the currents in the right rear quadrant of the hurricane. The reduction of the momentum flux into the ocean consequently reduces the magnitude of the subsurface current and sea surface temperature cooling to the right of the hurricane track and the rate of upwelling/downwelling in the thermocline. During wind–wave–current interaction, the momentum flux into the ocean is mainly affected by reducing the wind speed relative to currents, whereas the wave field is mostly affected by refraction due to the spatially varying currents. In the area where the current is strongly and roughly aligned with wave propagation direction, the wave spectrum of longer waves is reduced, the peak frequency is shifted to a higher frequency, and the angular distribution of the wave energy is widened.

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Raymond A. Richardson
,
Isaac Ginis
, and
Lewis M. Rothstein

Abstract

Numerical simulations of the local equatorial ocean response to idealized westerly wind burst (WWB) forcing are described. In particular, the authors examine the development and evolution of the subsurface westward jet (SSWJ) that has been observed to accompany these wind events. This westward current is interpreted as the signature of equatorial waves that accompany the downwelling and upwelling that occurs along the edges of the wind forcing region. Some important features of the SSWJ include maximum intensity toward the eastern edge of the forcing region, a time lag between the wind forcing and peak SSWJ development, and an eastward spreading of the SSWJ with time. The effect of wind burst zonal profile, magnitude, duration, and fetch on the SSWJ are explored. The response of an initially resting ocean to WWB forcing is compared with that for model oceans that are spun up with annual-mean surface fluxes and monthly varying fluxes. It is demonstrated that the gross features of the response for the spun up simulations can be well approximated by adding the background zonal current structure prior to the introduction of the wind burst to the initially resting ocean current response to the WWB. This result suggests that the zonal current structure that is present prior to the commencement of WWB forcing plays a key role in determining whether or not a SSWJ will develop.

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Georgi G. Sutyrin
,
Isaac Ginis
, and
Sergey A. Frolov

Abstract

Spatiotemporal evolution of a small localized meander on a Gulf Stream–type baroclinically unstable jet over a topographic slope is investigated numerically using a three-dimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent bottom layer over a positive (same sense as isopycnal tilt) cross-stream continental slope. A series of numerical experiments with the same initial conditions over a slope and flat bottom on the β plane and on the f plane has been carried out.

An initially localized meander evolves into a wave packet and generates deep eddies that provide a positive feedback for the meander growth. Meanders found growing over a flat bottom are able to pinch off resembling warm and cold core rings, while in the presence of a weak bottom slope such as 0.002, the maximum amplitudes of meanders and associated deep eddies saturate with no eddy shedding. In the flat bottom case, the growth rate is only 10% larger than in the weak slope case. Nevertheless, the bottom slope efficiently controls nonlinear saturation of meander growth via constraining the development of deep eddies. The topographic slope modifies the evolution of deep eddies and causes the phase displacement of deep eddies in the direction of the upper layer troughs/crests, thus limiting growth of the meanders. Behind the wave packet peak deep eddies form a nearly zonal circulation that stabilizes the jet in an equilibrated state. The main equilibration mechanism is a homogenization of the lower-layer potential vorticity by deep eddies. The width of the homogenized zone is narrower for a larger slope and/or on the β plane.

These results have the following implications to the Gulf Stream dynamics: 1) maximum of the meander amplitudes increase as the topographic slope relaxes in qualitative agreement with observed behavior of the Gulf Stream, 2) the phase locking of the meanders with deep eddies underneath at the nonlinear stage agrees qualitatively with the observed structure of large amplitude cyclonic troughs at the central array, and 3) the increase of the barotropic transport on the warm side of the jet and the generation of the recirculation on the cold side of the jet is consistent with observations in the Gulf Stream system downstream of Cape Hatteras.

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Brandon G. Reichl
,
Dong Wang
,
Tetsu Hara
,
Isaac Ginis
, and
Tobias Kukulka

Abstract

The Stokes drift of surface waves significantly modifies the upper-ocean turbulence because of the Craik–Leibovich vortex force (Langmuir turbulence). Under tropical cyclones the contribution of the surface waves varies significantly depending on complex wind and wave conditions. Therefore, turbulence closure models used in ocean models need to explicitly include the sea state–dependent impacts of the Langmuir turbulence. In this study, the K-profile parameterization (KPP) first-moment turbulence closure model is modified to include the explicit Langmuir turbulence effect, and its performance is tested against equivalent large-eddy simulation (LES) experiments under tropical cyclone conditions. First, the KPP model is retuned to reproduce LES results without Langmuir turbulence to eliminate implicit Langmuir turbulence effects included in the standard KPP model. Next, the Lagrangian currents are used in place of the Eulerian currents in the KPP equations that calculate the bulk Richardson number and the vertical turbulent momentum flux. Finally, an enhancement to the turbulent mixing is introduced as a function of the nondimensional turbulent Langmuir number. The retuned KPP, with the Lagrangian currents replacing the Eulerian currents and the turbulent mixing enhanced, significantly improves prediction of upper-ocean temperature and currents compared to the standard (unmodified) KPP model under tropical cyclones and shows improvements over the standard KPP at constant moderate winds (10 m s−1).

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Sergei A. Frolov
,
Georgi G. Sutyrin
, and
Isaac Ginis

Abstract

The symmetry properties of the Gulf Stream–type jet equilibrated over topographic slope are investigated in a series of idealized numerical experiments. A baroclinically unstable zonal jet equilibrates over a sloping bottom through the process of potential vorticity (PV) homogenization underneath the main thermocline by the bottom-intensified eddy activity associated with the stream meandering. Potential vorticity homogenization underneath the main thermocline leads to formation of recirculation gyres on both sides of the jet. The magnitude of the northern recirculation gyre, as measured by its westward transport, is larger than the magnitude of the southern recirculation gyre. This asymmetry in recirculations is shown to be the result of an asymmetric PV mixing underneath the thermocline produced by an asymmetric jet. In particular, the lateral shift of the velocity maximum near the surface relative to the velocity maximum at depth is shown to be responsible for the asymmetry. The results are related to the Gulf Stream data between 73° and 65°W.

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Dong Wang
,
Tobias Kukulka
,
Brandon G. Reichl
,
Tetsu Hara
, and
Isaac Ginis

Abstract

This study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves.

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Xiaohui Zhou
,
Tetsu Hara
,
Isaac Ginis
,
Eric D’Asaro
,
Je-Yuan Hsu
, and
Brandon G. Reichl

Abstract

The drag coefficient under tropical cyclones and its dependence on sea states are investigated by combining upper-ocean current observations [using electromagnetic autonomous profiling explorer (EM-APEX) floats deployed under five tropical cyclones] and a coupled ocean–wave (Modular Ocean Model 6–WAVEWATCH III) model. The estimated drag coefficient averaged over all storms is around 2–3 × 10−3 for wind speeds of 25–55 m s−1. While the drag coefficient weakly depends on wind speed in this wind speed range, it shows stronger dependence on sea states. In particular, it is significantly reduced when the misalignment angle between the dominant wave direction and the wind direction exceeds about 45°, a feature that is underestimated by current models of sea state–dependent drag coefficient. Since the misaligned swell is more common in the far front and in the left-front quadrant of the storm (in the Northern Hemisphere), the drag coefficient also tends to be lower in these areas and shows a distinct spatial distribution. Our results therefore support ongoing efforts to develop and implement sea state–dependent parameterizations of the drag coefficient in tropical cyclone conditions.

Open access
Dong Wang
,
Tobias Kukulka
,
Brandon G. Reichl
,
Tetsu Hara
,
Isaac Ginis
, and
Peter P. Sullivan

Abstract

Based on a large-eddy simulation approach, this study investigates the response of the ocean surface boundary layer (OSBL) and Langmuir turbulence (LT) to extreme wind and complex wave forcing under tropical cyclones (TCs). The Stokes drift vector that drives LT is determined from spectral wave simulations. During maximum TC winds, LT substantially enhances the entrainment of cool water, causing rapid OSBL deepening. This coincides with relatively strong wave forcing, weak inertial currents, and shallow OSBL depth , measured by smaller ratios of , where denotes a Stokes drift decay length scale. LT directly affects a near-surface layer whose depth is estimated from enhanced anisotropy ratios of velocity variances. During rapid OSBL deepening, is proportional to , and LT efficiently transports momentum in coherent structures, locally enhancing shear instabilities in a deeper shear-driven layer, which is controlled by LT. After the TC passes, inertial currents are stronger and is greater while is shallower and proportional to . During this time, the LT-affected surface layer is too shallow to directly influence the deeper shear-driven layer, so that both layers are weakly coupled. At the same time, LT reduces surface currents that play a key role in the surface energy input at a later stage. These two factors contribute to relatively small TKE levels and entrainment rates after TC passage. Therefore, our study illustrates that inertial currents need to be taken into account for a complete understanding of LT and its effects on OSBL dynamics in TC conditions.

Open access