Effect of Planetary Rotation on Oceanic Surface Boundary Layer Turbulence

AbstractA large-eddy simulation (LES) model is configured to investigate the effect of the horizontal (northward) component of Earth’s rotation on upper-ocean turbulence. The focus is on the variability of the effect with latitude/hemisphere in the presence of surface gravity waves and when capped by a stable stratification beneath the surface layer. When is included, the mean flow, turbulence, and vertical mixing depend on the wind direction. The value and effect of are the largest in the tropics and decrease with increasing latitudes. The variability in turbulent flows to wind direction is different at different latitudes and in opposite hemispheres. When limited by stable stratification, the variability in turbulence intensity to wind direction reduces, but the entrainment rate changes with wind direction. In wave-driven Langmuir turbulence, the variability in mean current to wind direction is reduced, but the variability of turbulence to wind direction is evident. When there is wind-following swell, the variability in the mean current to wind direction is further reduced. When there is strong wind-opposing swell so that the total wave forcing is opposite to the wind, the variability in the mean current to wind direction is reduced, but the variability of turbulence to wind direction is enhanced, compared to in Ekman turbulence. The profiles of eddy viscosity, including its shape and its value, show a strong wind direction dependence for both stratified wind-driven and wave-driven Langmuir turbulence. Our study demonstrates that wind direction is an important parameter to upper-ocean mixing, though it is overlooked in existing ocean models.

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Langmuir Turbulence in Swell

Journal of Physical Oceanography ◽

10.1175/jpo-d-13-0122.1 ◽

2014 ◽

Vol 44 (3) ◽

pp. 870-890 ◽

Cited By ~ 49

Author(s):

James C. McWilliams ◽

Edward Huckle ◽

Junhong Liang ◽

Peter P. Sullivan

Keyword(s):

Wave Amplitude ◽

Wind Waves ◽

Stress Profile ◽

Entrainment Rate ◽

Current Response ◽

Surface Boundary ◽

Oceanic Circulation ◽

Langmuir Turbulence ◽

Current Profile ◽

Mean Current

Abstract The problem is posed and solved for the oceanic surface boundary layer in the presence of wind stress, stable density stratification, equilibrium wind-waves, and remotely generated swell-waves. The addition of swell causes an amplification of the Lagrangian-mean current and rotation toward the swell-wave direction, a fattening of the Ekman velocity spiral and associated vertical Reynolds stress profile, an amplification of the inertial current response, an enhancement of turbulent variance and buoyancy entrainment rate from the pycnocline, and—for very large swell—an upscaling of the coherent Langmuir circulation patterns. Implications are discussed for the parameterization of Langmuir turbulence influences on the mean current profile and the material entrainment rate in oceanic circulation models. In particular, even though the turbulent kinetic energy monotonically increases with wave amplitude inversely expressed by the turbulent Langmuir number La, the Lagrangian shear eddy viscosity profile κL(z) is a nonmonotonic function of La, first increasing with increasing wave amplitude up to approximately the wind-wave equilibrium level, then decreasing with additional swell-wave amplitude. In contrast, the pycnocline entrainment rate is a monotonic function ~La−2.

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Langmuir turbulence and filament frontogenesis in the oceanic surface boundary layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.655 ◽

2019 ◽

Vol 879 ◽

pp. 512-553 ◽

Cited By ~ 1

Author(s):

Peter P. Sullivan ◽

James C. McWilliams

Keyword(s):

Boundary Layer ◽

Surface Waves ◽

Momentum Flux ◽

Shear Instability ◽

Small Scale ◽

Upper Ocean ◽

Surface Boundary ◽

Langmuir Turbulence ◽

Filament Axis ◽

Submesoscale Currents

Submesoscale currents, small-scale turbulence and surface gravity waves co-exist in the upper ocean and interact in complex ways. To expose the couplings, the frontogenetic life cycle of an idealized cold dense submesoscale filament interacting with upper ocean Langmuir turbulence is investigated in large-eddy simulations (LESs) based on the incompressible wave-averaged equations. The simulations utilize large domains and fine meshes with $6.4\times 10^{9}$ grid points. Case studies are made with surface winds or surface cooling with waves oriented in across-filament (perpendicular) or down-filament (parallel) directions relative to the two-dimensional filament axis. The currents $u$, $v$ and $w$ are aligned with the across-filament, down-filament and vertical directions, respectively. Frontogenesis is induced by across-filament Lagrangian secondary circulations in the boundary layer, and it is shown to be strongly impacted by surface waves, in particular the propagation direction relative to the filament axis. In a horizontally heterogeneous boundary layer, surface waves induce both mean and fluctuating Stokes-drift vortex forces that modify a linear, hydrostatic turbulent thermal wind (TTW) approximation for momentum. Down-filament winds and waves are found to be especially impactful, they significantly reduce the peak level of frontogenesis by fragmenting the filament into primary and secondary down-welling sites in a broad frontal zone over a width ${\sim}500~\text{m}$. At peak frontogenesis, opposing down-filament jets $\langle v\rangle$ overlie each other resulting in a vigorous vertical shear layer $\unicode[STIX]{x2202}_{z}\langle v\rangle$ with large vertical momentum flux $\langle v^{\prime }w^{\prime }\rangle$. Filament arrest is induced by a lateral shear instability that generates horizontal momentum flux $\langle u^{\prime }v^{\prime }\rangle$ at low wavenumbers. The turbulent vertical velocity patterns, indicative of coherent Langmuir cells, change markedly across the horizontal domain with both across-filament and down-filament winds under the action of submesoscale currents.

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The interaction of free Rossby waves with semi-transparent equatorial waveguide – wave-mean flow interaction

Nonlinear Processes in Geophysics ◽

10.5194/npg-16-381-2009 ◽

2009 ◽

Vol 16 (3) ◽

pp. 381-392 ◽

Cited By ~ 5

Author(s):

G. M. Reznik ◽

V. Zeitlin

Keyword(s):

Rossby Waves ◽

Landau Equation ◽

Spatial Modulation ◽

Equilibrium Solutions ◽

Mean Flow ◽

Ginzburg Landau ◽

Baroclinic Waves ◽

Ginzburg Landau Equation ◽

The Mean ◽

Mean Current

Abstract. Nonlinear interactions of the barotropic Rossby waves propagating across the equator with trapped baroclinic Rossby or Yanai modes and mean zonal flow are studied within the two-layer model of the atmosphere, or the ocean. It is shown that the equatorial waveguide with a mean current acts as a resonator and responds to barotropic waves with certain wavenumbers by making the trapped baroclinic modes grow. At the same time the equatorial waveguide produces the barotropic response which, via nonlinear interaction with the mean equatorial current and with the trapped waves, leads to the saturation of the growing modes. The excited baroclinic waves can reach significant amplitudes depending on the magnitude of the mean current. In the absence of spatial modulation the nonlinear saturation of thus excited waves is described by forced Landau-type equation with one or two attracting equilibrium solutions. In the latter case the spatial modulation of the baroclinic waves is expected to lead to the formation of characteristic domain-wall defects. The evolution of the envelopes of the trapped Rossby waves is governed by driven Ginzburg-Landau equation, while the envelopes of the Yanai waves obey the "first-order" forced Ginzburg-Landau equation. The envelopes of short baroclinic Rossby waves obey the damped-driven nonlinear Schrodinger equation well studied in the literature.

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A Parameterization with a Constrained Potential Energy Conversion Rate of Vertical Mixing Due to Langmuir Turbulence

Journal of Physical Oceanography ◽

10.1175/jpo-d-18-0258.1 ◽

2019 ◽

Vol 49 (11) ◽

pp. 2935-2959 ◽

Cited By ~ 5

Author(s):

Brandon G. Reichl ◽

Qing Li

Keyword(s):

Turbulent Mixing ◽

Vertical Mixing ◽

Stable Stratification ◽

Surface Boundary ◽

Langmuir Turbulence ◽

Surface Boundary Layer ◽

Eddy Simulation ◽

Available Energy ◽

Climate Simulations ◽

Surface Buoyancy

AbstractIn this study we develop a new parameterization for turbulent mixing in the ocean surface boundary layer (OSBL), including the effect of Langmuir turbulence. This new parameterization builds on a recent study (Reichl and Hallberg 2018, hereafter RH18), which predicts the available energy for turbulent mixing against stable stratification driven by shear and convective turbulence. To investigate the role of Langmuir turbulence in the framework of RH18, we utilize data from a suite of previously published large-eddy simulation (LES) experiments (Li and Fox-Kemper 2017, hereafter LF17) with and without Langmuir turbulence under different idealized forcing conditions. We find that the parameterization of RH18 is able to reproduce the mixing simulated by the LES in the non-Langmuir cases, but not the Langmuir cases. We therefore investigate the enhancement of the integrated vertical buoyancy flux within the entrainment layer in the presence of Langmuir turbulence using the LES data. An additional factor is introduced in the RH18 framework to capture the enhanced mixing due to Langmuir turbulence. This additional factor depends on the surface-layer averaged Langmuir number with a reduction in the presence of destabilizing surface buoyancy fluxes. It is demonstrated that including this factor within the RH18 OSBL turbulent mixing parameterization framework captures the simulated effect of Langmuir turbulence in the LES, which can be used for simulating the effect of Langmuir turbulence in climate simulations. This new parameterization is compared to the KPP-based Langmuir entrainment parameterization introduced by LF17, and differences are explored in detail.

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Assessing the Effects of Langmuir Turbulence on the Entrainment Buoyancy Flux in the Ocean Surface Boundary Layer

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0085.1 ◽

2017 ◽

Vol 47 (12) ◽

pp. 2863-2886 ◽

Cited By ~ 30

Author(s):

Qing Li ◽

Baylor Fox-Kemper

Keyword(s):

Boundary Layer ◽

Climate Model ◽

Ocean Surface ◽

Buoyancy Flux ◽

Entrainment Rate ◽

Surface Boundary ◽

Langmuir Turbulence ◽

Convective Turbulence ◽

Surface Boundary Layer ◽

The Impact

AbstractLarge-eddy simulations (LESs) with various constant wind, wave, and surface destabilizing surface buoyancy flux forcing are conducted, with a focus on assessing the impact of Langmuir turbulence on the entrainment buoyancy flux at the base of the ocean surface boundary layer. An estimate of the entrainment buoyancy flux scaling is made to best fit the LES results. The presence of Stokes drift forcing and the resulting Langmuir turbulence enhances the entrainment rate significantly under weak surface destabilizing buoyancy flux conditions, that is, weakly convective turbulence. In contrast, Langmuir turbulence effects are moderate when convective turbulence is dominant and appear to be additive rather than multiplicative to the convection-induced mixing. The parameterized unresolved velocity scale in the K-profile parameterization (KPP) is modified to adhere to the new scaling law of the entrainment buoyancy flux and account for the effects of Langmuir turbulence. This modification is targeted on common situations in a climate model where either Langmuir turbulence or convection is important and may overestimate the entrainment when both are weak. Nevertheless, the modified KPP is tested in a global climate model and generally outperforms those tested in previous studies. Improvements in the simulated mixed layer depth are found, especially in the Southern Ocean in austral summer.

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Mixed layer sub-mesoscale parameterization – Part 1: Derivation and assessment

Ocean Science ◽

10.5194/os-6-679-2010 ◽

2010 ◽

Vol 6 (3) ◽

pp. 679-693 ◽

Cited By ~ 8

Author(s):

V. M. Canuto ◽

M. S. Dubovikov

Keyword(s):

High Resolution ◽

Mixed Layer ◽

Wind Direction ◽

Small Scale ◽

Mean Flow ◽

Mean Velocity ◽

Geostrophic Velocity ◽

Global Circulation Models ◽

The Mean ◽

Strong Winds

Abstract. Several studies have shown that sub-mesoscales (SM ~1 km horizontal scale) play an important role in mixed layer dynamics. In particular, high resolution simulations have shown that in the case of strong down-front wind, the re-stratification induced by the SM is of the same order of the de-stratification induced by small scale turbulence, as well as of that induced by the Ekman velocity. These studies have further concluded that it has become necessary to include SM in ocean global circulation models (OGCMs), especially those used in climate studies. The goal of our work is to derive and assess an analytic parameterization of the vertical tracer flux under baroclinic instabilities and wind of arbitrary directions and strength. To achieve this goal, we have divided the problem into two parts: first, in this work we derive and assess a parameterization of the SM vertical flux of an arbitrary tracer for ocean codes that resolve mesoscales, M, but not sub-mesoscales, SM. In Part 2, presented elsewhere, we have used the results of this work to derive a parameterization of SM fluxes for ocean codes that do not resolve either M or SM. To carry out the first part of our work, we solve the SM dynamic equations including the non-linear terms for which we employ a closure developed and assessed in previous work. We present a detailed analysis for down-front and up-front winds with the following results: (a) down-front wind (blowing in the direction of the surface geostrophic velocity) is the most favorable condition for generating vigorous SM eddies; the de-stratifying effect of the mean flow and re-stratifying effect of SM almost cancel each other out, (b) in the up-front wind case (blowing in the direction opposite to the surface geostrophic velocity), strong winds prevents the SM generation while weak winds hinder the process but the eddies amplify the re-stratifying effect of the mean velocity, (c) wind orthogonal to the geostrophic velocity. In this case, which was not considered in numerical simulations, we show that when the wind direction coincides with that of the horizontal buoyancy gradient, SM eddies are generated and their re-stratifying effect partly cancels the de-stratifying effect of the mean velocity. The case when wind direction is opposite to that of the horizontal buoyancy gradient, is analogous to the case of up-front winds. In conclusion, the new multifaceted implications on the mixed layer stratification caused by the interplay of both strength and directions of the wind in relation to the buoyancy gradient disclosed by high resolution simulations have been reproduced by the present model. The present results can be used in OGCMs that resolve M but not SM.

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Strong Intraseasonal Variability of Meridional Currents near 5°N in the Eastern Indian Ocean: Characteristics and Causes

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0250.1 ◽

2017 ◽

Vol 47 (5) ◽

pp. 979-998 ◽

Cited By ~ 16

Author(s):

Gengxin Chen ◽

Weiqing Han ◽

Yuanlong Li ◽

Michael J. McPhaden ◽

Ju Chen ◽

...

Keyword(s):

Indian Ocean ◽

Rossby Waves ◽

Intraseasonal Variability ◽

Upper Ocean ◽

Mean Flow ◽

Eastern Boundary ◽

Typical Period ◽

The Indian Ocean ◽

The Mean

AbstractThis paper reports on strong, intraseasonal, upper-ocean meridional currents observed in the Indian Ocean between the Bay of Bengal (BOB) and the equator and elucidates the underlying physical processes responsible for them. In situ measurements from a subsurface mooring at 5°N, 90.5°E reveal strong intraseasonal variability of the meridional current with an amplitude of ~0.4 m s−1 and a typical period of 30–50 days in the upper 150 m, which by far exceeds the magnitudes of the mean flow and seasonal cycle. Such prominent intraseasonal variability is, however, not seen in zonal current at the same location. Further analysis suggests that the observed intraseasonal flows are closely associated with westward-propagating eddylike sea surface height anomalies (SSHAs) along 5°N. The eddylike SSHAs are largely manifestations of symmetric Rossby waves, which result primarily from intraseasonal wind stress forcing in the equatorial waveguide and reflection of the equatorial Kelvin waves at the eastern boundary. Since the wave signals are generally symmetric about the equator, similar variability is also seen at 5°S but with weaker intensity because of the inclined coastline at the eastern boundary. The Rossby waves propagate westward, causing pronounced intraseasonal SSHA and meridional current in the upper ocean across the entire southern BOB between 84° and 94°E. They greatly weaken in the western Indian Basin, but zonal currents near the equator remain relatively strong.

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Gulf Stream Dynamics along the Southeastern U.S. Seaboard

Journal of Physical Oceanography ◽

10.1175/jpo-d-14-0154.1 ◽

2015 ◽

Vol 45 (3) ◽

pp. 690-715 ◽

Cited By ~ 69

Author(s):

Jonathan Gula ◽

M. Jeroen Molemaker ◽

James C. McWilliams

Keyword(s):

Gulf Stream ◽

Ocean Modeling ◽

Mean Flow ◽

Regional Ocean Modeling System ◽

Meridional Transport ◽

Local Pressure ◽

Straits Of Florida ◽

Eddy Fluxes ◽

The Mean ◽

Mean Current

AbstractThe Gulf Stream strongly interacts with the topography along the southeastern U.S. seaboard, between the Straits of Florida and Cape Hatteras. The dynamics of the Gulf Stream in this region is investigated with a set of realistic, very high-resolution simulations using the Regional Ocean Modeling System (ROMS). The mean path is strongly influenced by the topography and in particular the Charleston Bump. There are significant local pressure anomalies and topographic form stresses exerted by the bump that retard the mean flow and steer the mean current pathway seaward. The topography provides, through bottom pressure torque, the positive input of barotropic vorticity necessary to balance the meridional transport of fluid and close the gyre-scale vorticity balance. The effect of the topography on the development of meanders and eddies is studied by computing energy budgets of the eddies and the mean flow. The baroclinic instability is stabilized by the slope everywhere except past the bump. The flow is barotropically unstable, and kinetic energy is converted from the mean flow to the eddies following the Straits of Florida and at the bump with regions of eddy-to-mean conversion in between. There is eddy growth by Reynolds stress and downstream development of the eddies. Interaction of the flow with the topography acts as an external forcing process to localize these oceanic storm tracks. Associated time-averaged eddy fluxes are essential to maintain and reshape the mean current. The pattern of eddy fluxes is interpreted in terms of eddy life cycle, eddy fluxes being directed downgradient in eddy growth regions and upgradient in eddy decay regions.

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Turbulent diffusion near a free surface

Journal of Fluid Mechanics ◽

10.1017/s0022112099007466 ◽

2000 ◽

Vol 407 ◽

pp. 145-166 ◽

Cited By ~ 27

Author(s):

LIAN SHEN ◽

GEORGE S. TRIANTAFYLLOU ◽

DICK K. P. YUE

Keyword(s):

Boundary Layer ◽

Free Surface ◽

Turbulent Diffusion ◽

Similarity Solution ◽

Stokes Equations ◽

Numerical Study ◽

Turbulent Shear ◽

Surface Boundary ◽

Mean Flow ◽

The Mean

We study numerically and analytically the turbulent diffusion characteristics in a low-Froude-number turbulent shear flow beneath a free surface. In the numerical study, the Navier–Stokes equations are solved directly subject to viscous boundary conditions at the free surface. From an ensemble of such simulations, we find that a boundary layer develops at the free surface characterized by a fast reduction in the value of the eddy viscosity. As the free surface is approached, the magnitude of the mean shear initially increases over the boundary (outer) layer, reaches a maximum and then drops to zero inside a much thinner inner layer. To understand and model this behaviour, we derive an analytical similarity solution for the mean flow. This solution predicts well the shape and the time-scaling behaviour of the mean flow obtained in the direct simulations. The theoretical solution is then used to derive scaling relations for the thickness of the inner and outer layers. Based on this similarity solution, we propose a free-surface function model for large-eddy simulations of free-surface turbulence. This new model correctly accounts for the variations of the Smagorinsky coefficient over the free-surface boundary layer and is validated in both a priori and a posteriori tests.

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