Langmuir turbulence in the ocean

1997 ◽  
Vol 334 ◽  
pp. 1-30 ◽  
Author(s):  
JAMES C. McWILLIAMS ◽  
PETER P. SULLIVAN ◽  
CHIN-HOH MOENG
Keyword(s):  
Volume Transport ◽  
Stokes Drift ◽  
Equilibrium Solutions ◽  
Vertical Fluxes ◽  
Averaged Equations ◽  
Large Eddy ◽  
Convergence Zones ◽  
The Right ◽  
Langmuir Cells ◽  
Oceanic Currents

Solutions are analysed from large-eddy simulations of the phase-averaged equations for oceanic currents in the surface planetary boundary layer (PBL), where the averaging is over high-frequency surface gravity waves. These equations have additional terms proportional to the Lagrangian Stokes drift of the waves, including vortex and Coriolis forces and tracer advection. For the wind-driven PBL, the turbulent Langmuir number, Latur = (U∗/Us)1/2, measures the relative influences of directly wind-driven shear (with friction velocity U∗) and the Stokes drift Us. We focus on equilibrium solutions with steady, aligned wind and waves and a realistic Latur = 0.3. The mean current has an Eulerian volume transport to the right of the wind and against the Stokes drift. The turbulent vertical fluxes of momentum and tracers are enhanced by the presence of the Stokes drift, as are the turbulent kinetic energy and its dissipation and the skewness of vertical velocity. The dominant coherent structure in the turbulence is a Langmuir cell, which has its strongest vorticity aligned longitudinally (with the wind and waves) and intensified near the surface on the scale of the Stokes drift profile. Associated with this are down-wind surface convergence zones connected to interior circulations whose horizontal divergence axis is rotated about 45° to the right of the wind. The horizontal scale of the Langmuir cells expands with depth, and there are also intense motions on a scale finer than the dominant cells very near the surface. In a turbulent PBL, Langmuir cells have irregular patterns with finite correlation scales in space and time, and they undergo occasional mergers in the vicinity of Y-junctions between convergence zones.

scholarly journals Turbulence-Induced Anti-Stokes Flow and the Resulting Limitations of Large-Eddy Simulation

2018 ◽  
Vol 48 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Brodie Pearson
Keyword(s):  
Stokes Flow ◽  
Energy Production ◽  
Surface Wind ◽  
Stokes Drift ◽  
Near Surface ◽  
Eddy Simulation ◽  
Surface Wind Stress ◽  
Planetary Rotation ◽  
Large Eddy ◽  
Anti Stokes

AbstractThis study shows that the presence of Stokes drift us in the turbulent upper ocean induces a near-surface Eulerian current that opposes the Stokes drift. This current is distinct from previously studied anti-Stokes currents because it does not rely on the presence of planetary rotation or mean lateral gradients. Instead, the anti-Stokes flow arises from an interaction between the Stokes drift and turbulence. The new anti-Stokes flow is antiparallel to us near the ocean surface, is parallel to us at depth, and integrates to zero over the depth of the boundary layer. The presence of Stokes drift in large-eddy simulations (LES) is shown to induce artificial energy production caused by a combination of the new anti-Stokes flow and LES numerics. As a result, care must be taken when designing and interpreting simulations of realistic wave forcing, particularly as rotation becomes weak and/or us becomes perpendicular to the surface wind stress. The mechanism of the artificial energy production is demonstrated for a generalized LES subgrid scheme.

scholarly journals Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow

2017 ◽  
Vol 827 ◽  
pp. 225-249 ◽  
Author(s):  
Atsushi Sekimoto ◽  
Javier Jiménez
Keyword(s):  
Shear Flow ◽  
Vertical Direction ◽  
Large Eddy Simulations ◽  
Small Scale ◽  
Box Dimension ◽  
Equilibrium Solutions ◽  
Vortical Structures ◽  
Homogeneous Shear ◽  
Large Eddy ◽  
Homogeneous Shear Flow

Unstable equilibrium solutions in a homogeneous shear flow with sinuous (streamwise-shift-reflection and spanwise-shift-rotation) symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_{S}$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_{z}$. The fraction $R_{S}=L_{z}/l_{S}$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $R_{S}$ increases, and that the flow structures resemble those in plane Couette flow with the same sinuous symmetry. The vortical structures of both lower- and upper-branch solutions become spontaneously localised in the vertical direction. The lower-branch solution is an edge state at low $R_{S}$, and takes the form of a thin critical layer as $R_{S}$ increases, as in the asymptotic theory of generic shear flow at high Reynolds numbers. On the other hand, the upper-branch solutions are characterised by a tall velocity streak with multiscale multiple vortical structures. At the higher end of $R_{S}$, an incipient multiscale structure is found. The LES turbulence occasionally visits vertically localised states whose vortical structure resembles the present vertically localised LES equilibria.

Disruption of the bottom log layer in large-eddy simulations of full-depth Langmuir circulation

2012 ◽  
Vol 699 ◽  
pp. 79-93 ◽  
Author(s):  
A. E. Tejada-Martínez ◽  
C. E. Grosch ◽  
N. Sinha ◽  
C. Akan ◽  
G. Martinat
Keyword(s):  
Gravity Waves ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Navier Stokes ◽  
Wake Region ◽  
Langmuir Circulation ◽  
Mean Velocity ◽  
Wave Forcing ◽  
Large Eddy ◽  
Shear Current

AbstractWe report on disruption of the log layer in the resolved bottom boundary layer in large-eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter-rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analysed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log-law profile within the range $90\lt { x}_{3}^{+ } \lt 200$. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications for turbulence parameterizations for Reynolds-averaged Navier–Stokes simulations of the coastal ocean.

scholarly journals Impact of Wind Veer and the Coriolis Force for an Idealized Farm to Farm Interaction Case

2019 ◽  
Vol 9 (5) ◽  
pp. 922 ◽  
Author(s):  
Ola Eriksson ◽  
Simon-Philippe Breton ◽  
Karl Nilsson ◽  
Stefan Ivanell
Keyword(s):  
Coriolis Force ◽  
Wind Shear ◽  
Source Term ◽  
Wind Farms ◽  
Long Distance ◽  
Large Eddy ◽  
Relative Production ◽  
The Mean ◽  
The Right ◽  
The Impact

The impact of the Coriolis force on the long distance wake behind wind farms is investigated using Large Eddy Simulations (LES) combined with a Forced Boundary Layer (FBL) technique. When using the FBL technique any mean wind shear and turbulent fluctuations can be added with body forces. The wind shear can also include the mean wind veer due to the Coriolis force. The variation of the Coriolis force due to local deviations from the mean profile, e.g., from wakes, is not taken into account in the FBL. This can be corrected for with an extra source term in the equations, hereon defined as the Coriolis correction. For a row of 4 turbines it is shown that the inclusion of the wind veer turns the wake to the right, while including the Coriolis correction turns it to the left. When including both wind veer and Coriolis correction the impact of wind veer dominates. For an idealized farm to farm interaction case, two farms of 4 ∗ 4 turbines with 6 km in between, it can be seen that when including wind veer and the Coriolis correction a approximately 3% increase in the relative production for a full wake direction can be seen and only a slightly smaller increase can be seen when including only wind veer. The results indicate that FBL can be used for studies of long distance wakes without including a Coriolis correction but efforts need to be taken to use a wind shear with a correct mean wind veer.

scholarly journals Contrasting Hydrodynamic Responses to Atmospheric Systems with Different Scales: Impact of Cold Fronts vs. That of a Hurricane

2020 ◽  
Vol 8 (12) ◽  
pp. 979
Author(s):  
Wei Huang ◽  
Chunyan Li
Keyword(s):  
Water Level ◽  
Cold Front ◽  
Volume Transport ◽  
Water Volume ◽  
Cold Fronts ◽  
Barataria Bay ◽  
Before And After ◽  
Frequent Exchange ◽  
The Right ◽  
Mexico Coast

In this paper, subtidal responses of Barataria Bay to an atmospheric cold front in 2014 and Hurricane Barry of 2019 are studied. The cold fronts had shorter influencing periods (1 to 3 days), while Hurricane Barry had a much longer influencing period (about 1 week). Wind direction usually changes from southern quadrants to northern quadrants before and after a cold front’s passage. For a hurricane making its landfall at the norther Gulf of Mexico coast, wind variation is dependent on the location relative to the location of landfall. Consequently, water level usually reaches a trough after the maximum cold front wind usually; while after the maximum wind during a hurricane, water level mostly has a surge, especially on the right-hand side of the hurricane. Water level variation induced by Hurricane Barry is about 3 times of that induced by a cold front event. Water volume flux also shows differences under these two weather types: the volume transport during Hurricane Barry was 4 times of that during a cold front. On the other hand, cold front events are much more frequent (30–40 times a year), and they lead to more frequent exchange between Barataria Bay and the coastal ocean.

Langmuir turbulence in shallow water. Part 1. Observations

2007 ◽  
Vol 576 ◽  
pp. 27-61 ◽  
Author(s):  
ANN E. GARGETT ◽  
JUDITH R. WELLS
Keyword(s):  
Shallow Water ◽  
Turbulent Flows ◽  
Deep Water ◽  
Vertical Velocity ◽  
Surface Stress ◽  
Large Eddy Simulations ◽  
Wave Groups ◽  
Large Eddy ◽  
Langmuir Circulations ◽  
Langmuir Cells

During extended deployment at an ocean observatory off the coast of New Jersey, a bottom-mounted five-beam acoustic Doppler current profiler measured large-scale velocity structures that we interpret as Langmuir circulations filling the entire water column. These circulations are the large-eddy structures of wind-wave-driven turbulent flows that occur episodically when a shallow water column experiences prolonged strong wind forcing. Many observational characteristics agree with former descriptions of Langmuir circulations in deep water. The three-dimensional velocity field reveals quasi-organized structures consisting of pairs of surface-intensified counter-rotating vortices, aligned approximately downwind. Maximum downward velocities are stronger than upward velocities, and the downwelling region of each cell, defined as a pair of vortices, is narrower than the upwelling region. Maximum downward vertical velocity occurs at or above mid-depth, and scales approximately with wind speed. The estimated crosswind scale of cells is roughly 3–6 times their vertical scale, set under these conditions by water depth. The long axis of the cells appears to lie at an angle ∼10°–20° to the right of the wind. A major difference from deep-water observations is strong near-bottom intensification of the downwind ‘jets’ found typically centred over downwelling regions. Accessible observational features such as cell morphology and profiles of mean velocities, turbulent velocity variances, and shear stress components are compared with the results of associated large-eddy simulations (reported in Part 2) of shallow water flows driven by surface stress and the Craik–Leibovich vortex forcing generally used to represent generation of Langmuir cells. A particularly sensitive diagnostic for identification of Langmuir circulations as the energy-containing eddies of the turbulent flow is the depth trajectory of invariants of the turbulent stress tensor, plotted in the Lumley ‘triangle’ corresponding to realizable turbulent flows. When Langmuir structures are present in the observations, the Lumley map is distinctly different from that of surface-stress-driven Couette flow, again in agreement with the large-eddy simulations (LES). Unlike the LES, observed velocity fields contain two distinct and significant scales of variability, documented by wavelet analysis of observational records of vertical velocity. Variability with periods of many minutes is that expected from Langmuir cells drifting past the instrument at the slowly time-varying crosswind velocity. Shorter period variability, of the order of 1–2 min, has roughly the observed periodicity of surface wave groups, suggesting a connection with the wave groups themselves and/or the wave breaking associated with them in high wind conditions.

scholarly journals Symmetric and Geostrophic Instabilities in the Wave-Forced Ocean Mixed Layer

2015 ◽  
Vol 45 (12) ◽  
pp. 3033-3056 ◽  
Author(s):  
Sean Haney ◽  
Baylor Fox-Kemper ◽  
Keith Julien ◽  
Adrean Webb
Keyword(s):  
Coriolis Force ◽  
Potential Vorticity ◽  
Shear Force ◽  
Baroclinic Instability ◽  
Boussinesq Equations ◽  
Stokes Drift ◽  
Ocean Mixed Layer ◽  
Large Eddy ◽  
Balanced Flow ◽  
Anti Stokes

AbstractHere, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.

The generation of Langmuir circulations by an instability mechanism

1977 ◽  
Vol 81 (2) ◽  
pp. 209-223 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Continuous Wave ◽  
Current System ◽  
Plane Waves ◽  
Wave Spectrum ◽  
Stokes Drift ◽  
Instability Mechanism ◽  
Fluid Layers ◽  
The Mean ◽  
Langmuir Cells ◽  
Relationship Of

Equations governing the current system in the upper layers of oceans and lakes were derived by Craik & Leibovich (1976). These incorporate the dominant effects of both wind and waves. Solutions comprising the mean wind-driven current and a system of ‘Langmuir’ cells aligned parallel to the wind were found for cases in which the wave field consisted of just a pair of plane waves. However, it was not clear that such cellular motions would persist for the more realistic case of a continuous wave spectrum.The present paper shows that, in the latter case, infinitesimal spanwise periodic perturbations will grow on account of an instability mechanism. Mathematically, the instability is closely similar to the onset of thermal convection in horizontal fluid layers. Physically, the mechanism is governed by kinematical processes involving the mean (Eulerian) wind-driven current and the (Lagrangian) Stokes drift associated with the waves. The relationship of this mechanism to instability models of Garrett and Gammelsrød is clarified.

scholarly journals Reply to “Comment on ‘Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters’”

2017 ◽  
Vol 34 (6) ◽  
pp. 1391-1392
Author(s):  
A. D. Greene ◽  
P. J. Hendricks ◽  
M. C. Gregg
Keyword(s):  
Coastal Waters ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Stratified Turbulence ◽  
Dominant Mechanism ◽  
Turbulent Dissipation ◽  
Velocity Estimate ◽  
Horizontal Length ◽  
Large Eddy ◽  
Langmuir Cells

AbstractThis note is a comment in response to Gargett, who argues that a large-eddy estimate of turbulent dissipation rate using a horizontal length scale with a vertical velocity estimate, as in Greene et al., is a dubious approximation if the energy-containing eddies are anisotropic. A simulation of Langmuir cells and associated turbulence is used to support Gargett’s conclusions. This rebuttal reviews the approaches taken by Greene et al. and cites several instances of flawed reasoning by Gargett. This includes using Langmuir simulations to support the primary conclusion of Gargett, which seems unconnected to Greene et al.’s data and ignores a vast body of work on simulating Kelvin–Helmholtz instabilities, widely considered to be the dominant mechanism producing stratified turbulence.

scholarly journals A Theoretical Analysis of Mixing Length for Atmospheric Models From Micro to Large Scales

2021 ◽  
Vol 8 ◽  
Author(s):  
Rachel Honnert ◽  
Valéry Masson ◽  
Christine Lac ◽  
Tim Nagel
Keyword(s):  
Boundary Layer ◽  
Isotropic Turbulence ◽  
Atmospheric Model ◽  
Large Eddy Simulations ◽  
Mixing Length ◽  
Gray Zone ◽  
Convective Boundary ◽  
Homogeneity Assumption ◽  
Large Eddy ◽  
The Right

A new mixing length adapted to the constraints of the hectometric-scale gray zone of turbulence for neutral and convective boundary layers is proposed. It combines a mixing length for mesoscale simulations, where the turbulence is fully subgrid and a mixing length for Large-Eddy Simulations, where the coarsest turbulent eddies are explicitly resolved. The mixing length is built for isotropic turbulence schemes, as well as schemes using the horizontal homogeneity assumption. This mixing length is tested over three boundary layer cases: a free convective case, a neutral case and a cold air outbreak case. The later combines turbulence from thermal and dynamical origins as well as presence of clouds. With this new mixing length, the turbulence scheme produces the right proportion between subgrid and resolved turbulent exchanges in Large Eddy Simulations, in the gray zone and at the mesoscale. This opens the way of using a single mixing length whatever the grid mesh of the atmospheric model, the evolution stage or the depth of the boundary layer.

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