scholarly journals Large-Eddy Simulation of Langmuir Turbulence in Pure Wind Seas

2008 ◽  
Vol 38 (7) ◽  
pp. 1542-1562 ◽  
Author(s):  
Ramsey R. Harcourt ◽  
Eric A. D’Asaro
Keyword(s):  
Surface Layer ◽  
Surface Wave ◽  
Mixed Layer ◽  
Wave Spectrum ◽  
Vertical Component ◽  
Phase Speed ◽  
Relative Magnitude ◽  
Stokes Drift ◽  
Wave Age ◽  
Large Eddy

Abstract The scaling of turbulent kinetic energy (TKE) and its vertical component (VKE) in the upper ocean boundary layer, forced by realistic wind stress and surface waves including the effects of Langmuir circulations, is investigated using large-eddy simulations (LESs). The interaction of waves and turbulence is modeled by the Craik–Leibovich vortex force. Horizontally uniform surface stress τ0 and Stokes drift profiles uS(z) are specified from the 10-m wind speed U10 and the surface wave age CP/U10, where CP is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age–dependent neutral drag coefficient CD. Wave-breaking effects are not otherwise included. Mixed layer depths HML vary from 30 to 120 m, with 0.6 ≤ CP/U10 ≤ 1.2 and 8 m s−1 < U10 < 70 m s−1, thereby addressing most possible oceanic conditions where TKE production is dominated by wind and wave forcing. The mixed layer–averaged “bulk” VKE 〈w2〉/u*2 is equally sensitive to the nondimensional Stokes e-folding depth D*S/HML and to the turbulent Langmuir number Lat = u*/US, where u* = |τ0|/ρw in water density ρw and US = |uS|z=0. Use of a D*S scale-equivalent monochromatic wave does not accurately reproduce the results using a full-surface wave spectrum with the same e-folding depth. The bulk VKE for both monochromatic and broadband spectra is accurately predicted using a surface layer (SL) Langmuir number LaSL = u*/〈uS〉SL, where 〈uS〉SL is the average Stokes drift in a surface layer 0 > z > − 0.2HML relative to that near the bottom of the mixed layer. In the wave-dominated limit LaSL → 0, turbulent vertical velocity scales as wrms ∼ u*La−2/3SL. The mean profile (z) of VKE is characterized by a subsurface peak, the depth of which increases with D*S/HML to a maximum near 0.22HML as its relative magnitude /〈w2〉 decreases. Modestly accurate scalings for these variations are presented. The magnitude of the crosswind velocity convergence scales differently from VKE. These results predict that for pure wind seas and HML ≅ 50 m, 〈w2〉/u*2 varies from less than 1 for young waves at U10 = 10 m s−1 to about 2 for mature seas at winds greater than U10 = 30 m s−1. Preliminary comparisons with Lagrangian float data account for invariance in 〈w2〉/u*2 measurements as resulting from an inverse relationship between U10 and CP/U10 in observed regimes.

scholarly journals Similarity Theory in the Surface Layer of Large-Eddy Simulations of the Wind-, Wave-, and Buoyancy-Forced Southern Ocean

2019 ◽  
Vol 49 (8) ◽  
pp. 2165-2187 ◽  
Author(s):  
William G. Large ◽  
Edward G. Patton ◽  
Alice K. DuVivier ◽  
Peter P. Sullivan ◽  
Leonel Romero
Keyword(s):  
Surface Layer ◽  
Southern Ocean ◽  
Wind Wave ◽  
Similarity Theory ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Total Production ◽  
Similarity Functions ◽  
Wide Range ◽  
Large Eddy

AbstractMonin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.

scholarly journals Langmuir–Submesoscale Interactions: Descriptive Analysis of Multiscale Frontal Spindown Simulations

2014 ◽  
Vol 44 (9) ◽  
pp. 2249-2272 ◽  
Author(s):  
Peter E. Hamlington ◽  
Luke P. Van Roekel ◽  
Baylor Fox-Kemper ◽  
Keith Julien ◽  
Gregory P. Chini
Keyword(s):  
Surface Wave ◽  
Mixed Layer ◽  
Potential Vorticity ◽  
Mixed Layer Depth ◽  
Descriptive Analysis ◽  
Boussinesq Equations ◽  
Stokes Drift ◽  
Small Scale ◽  
Langmuir Turbulence ◽  
Layer Depth

Abstract The interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also shown to be in good agreement with results from an asymptotic analysis of the surface-wave-averaged, or Craik–Leibovich, equations. Regions of potential instability in the flow are identified using Richardson and Rossby numbers, and it is found that mixed gravitational/symmetric instabilities are nearly twice as prevalent when Langmuir turbulence is present, in contrast to simulations without Stokes drift forcing, which are dominated by symmetric instabilities. Mixed layer depth calculations based on potential vorticity and temperature show that the mixed layer is up to 2 times deeper in the presence of Langmuir turbulence. Differences between measures of the mixed layer depth based on potential vorticity and temperature are smaller in the simulations with Stokes drift forcing, indicating a reduced incidence of symmetric instabilities in the presence of Langmuir turbulence.

Surface Wave Effects on High-Frequency Currents over a Shelf Edge Bank

2013 ◽  
Vol 43 (8) ◽  
pp. 1627-1647 ◽  
Author(s):  
H. W. Wijesekera ◽  
D. W. Wang ◽  
W. J. Teague ◽  
E. Jarosz ◽  
W. E. Rogers ◽  
...  
Keyword(s):  
Surface Wave ◽  
Kinetic Energy ◽  
Mixed Layer ◽  
High Frequency ◽  
Pressure Sensors ◽  
Stokes Drift ◽  
Langmuir Circulation ◽  
Temperature Conductivity ◽  
Wave Focusing ◽  
Wave Effects

Abstract Several acoustic Doppler current profilers and vertical strings of temperature, conductivity, and pressure sensors, deployed on and around the East Flower Garden Bank (EFGB), were used to examine surface wave effects on high-frequency flows over the bank and to quantify spatial and temporal characteristic of these high-frequency flows. The EFGB, about 5-km wide and 10-km long, is located about 180-km southeast of Galveston, Texas, and consists of steep slopes on southern and eastern sides that rise from water depths over 100 m to within 20 m of the surface. Three-dimensional flows with frequencies ranging from 0.2 to 2 cycles per hour (cph) were observed in the mixed layer when wind speed and Stokes drift at the surface were large. These motions were stronger over the bank than outside the perimeter. The squared vertical velocity w2 was strongest near the surface and decayed exponentially with depth, and the e-folding length of w2 was 2 times larger than that of Stokes drift. The 2-h-averaged w2 in the mixed layer, scaled by the squared friction velocity, was largest when the turbulent Langmuir number was less than unity and the mixed layer was shallow. It is suggested that Langmuir circulation is responsible for the generation of vertical flows in the mixed layer, and that the increase in kinetic energy is due to an enhancement of Stokes drift by wave focusing. The lack of agreement with open-ocean Langmuir scaling arguments is likely due to the enhanced kinetic energy by wave focusing.

Estimates of Surface Waves Using Subsurface EM-APEX Floats under Typhoon Fanapi 2010

2018 ◽  
Vol 35 (5) ◽  
pp. 1053-1075 ◽  
Author(s):  
Je-Yuan Hsu ◽  
Ren-Chieh Lien ◽  
Eric A. D’Asaro ◽  
Thomas B. Sanford
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Spectrum ◽  
Nonlinear Least Squares ◽  
Peak Frequency ◽  
Wave Propagation Direction ◽  
Model Studies ◽  
Surface Wave Propagation ◽  
Left Quadrant ◽  
Field Inclination

AbstractSeven subsurface Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats measured the voltage induced by the motional induction of seawater under Typhoon Fanapi in 2010. Measurements were processed to estimate high-frequency oceanic velocity variance associated with surface waves. Surface wave peak frequency fp and significant wave height Hs are estimated by a nonlinear least squares fitting to , assuming a broadband JONSWAP surface wave spectrum. The Hs is further corrected for the effects of float rotation, Earth’s geomagnetic field inclination, and surface wave propagation direction. The fp is 0.08–0.10 Hz, with the maximum fp of 0.10 Hz in the rear-left quadrant of Fanapi, which is ~0.02 Hz higher than in the rear-right quadrant. The Hs is 6–12 m, with the maximum in the rear sector of Fanapi. Comparing the estimated fp and Hs with those assuming a single dominant surface wave yields differences of more than 0.02 Hz and 4 m, respectively. The surface waves under Fanapi simulated in the WAVEWATCH III (ww3) model are used to assess and compare to float estimates. Differences in the surface wave spectra of JONSWAP and ww3 yield uncertainties of <5% outside Fanapi’s eyewall and >10% within the eyewall. The estimated fp is 10% less than the simulated before the passage of Fanapi’s eye and 20% less after eye passage. Most differences between Hs and simulated are <2 m except those in the rear-left quadrant of Fanapi, which are ~5 m. Surface wave estimates are important for guiding future model studies of tropical cyclone wave–ocean interactions.

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.

Oceanic wave-balanced surface fronts and filaments

2013 ◽  
Vol 730 ◽  
pp. 464-490 ◽  
Author(s):  
James C. McWilliams ◽  
Baylor Fox-Kemper
Keyword(s):  
Mixed Layer ◽  
Stokes Drift ◽  
Surface Gravity Wave ◽  
Initial Flow ◽  
Coriolis Forces ◽  
Flow Perturbation ◽  
Front Shape ◽  
Oceanic Wave ◽  
Mixed Layers ◽  
Layer Deformation

AbstractA geostrophic, hydrostatic, frontal or filamentary flow adjusts conservatively to accommodate a surface gravity wave field with wave-averaged, Stokes-drift vortex and Coriolis forces in an altered balanced state. In this altered state, the wave-balanced perturbations have an opposite cross-front symmetry to the original geostrophic state; e.g. the along-front flow perturbation is odd-symmetric about the frontal centre while the geostrophic flow is even-symmetric. The adjustment tends to make the flow scale closer to the deformation radius, and it induces a cross-front shape displacement in the opposite direction to the overturning effects of wave-aligned down-front and up-front winds. The ageostrophic, non-hydrostatic, adjusted flow may differ from the initial flow substantially, with velocity and buoyancy perturbations that extend over a larger and deeper region than the initial front and Stokes drift. The largest effect occurs for fronts that are wider than the mixed layer deformation radius and that fill about two-thirds of a well-mixed surface layer, with the Stokes drift spanning only the shallowest part of the mixed layer. For even deeper mixed layers, and especially for thinner or absent mixed layers, the wave-balanced adjustments are not as large.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

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 Energetic Submesoscales Maintain Strong Mixed Layer Stratification during an Autumn Storm

2017 ◽  
Vol 47 (10) ◽  
pp. 2419-2427 ◽  
Author(s):  
Daniel B. Whitt ◽  
John R. Taylor
Keyword(s):  
Mixed Layer ◽  
North Atlantic ◽  
Small Scale ◽  
Upper Ocean ◽  
Ocean Mixed Layer ◽  
Ocean Stratification ◽  
The North ◽  
Large Eddy ◽  
The Mean ◽  
Scale Turbulence

AbstractAtmospheric storms are an important driver of changes in upper-ocean stratification and small-scale (1–100 m) turbulence. Yet, the modifying effects of submesoscale (0.1–10 km) motions in the ocean mixed layer on stratification and small-scale turbulence during a storm are not well understood. Here, large-eddy simulations are used to study the coupled response of submesoscale and small-scale turbulence to the passage of an idealized autumn storm, with a wind stress representative of a storm observed in the North Atlantic above the Porcupine Abyssal Plain. Because of a relatively shallow mixed layer and a strong downfront wind, existing scaling theory predicts that submesoscales should be unable to restratify the mixed layer during the storm. In contrast, the simulations reveal a persistent and strong mean stratification in the mixed layer both during and after the storm. In addition, the mean dissipation rate remains elevated throughout the mixed layer during the storm, despite the strong mean stratification. These results are attributed to strong spatial variability in stratification and small-scale turbulence at the submesoscale and have important implications for sampling and modeling submesoscales and their effects on stratification and turbulence in the upper ocean.

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