Mixing driven by vertically variable forcing: an application to the case of Langmuir circulation

Gnanadesikan, Anand

doi:10.1017/s0022112096002716

Cited by 11 publications

(6 citation statements)

References 16 publications

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“…This increases the Stokes drift shear, but only near the surface, while decreasing it at depth. Comparison of the PM and monochromatic growth rates without rescaling (which is equivalent to a larger shear ratio) shows the increase for the PM case, which agrees with Gnanadesikan [1996].…”

Section: The Reason That the Stokes Drift Is Less Effective In Alignisupporting

confidence: 77%

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Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift

Polonichko¹

1997

J. Geophys. Res.

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The growth rate of Langmuir cells is calculated from a linear stability analysis for different orientations of wind, waves, and cells as well as for various values of the dimensionless parameters describing wave-current interaction. These parameters could be the Stokes drift/friction velocity ratio and the shear ratio Sr which describes the relative strength of the Stokes drift shear and mean Eulerian shear. The growth rate is maximal overall when wind and waves are aligned. For a given angle between the Stokes drift and the wind (the misalignment angle), the direction of the cell axis for maximal growth lies between wind and waves and is mainly determined by (1) the misalignment angle and (2) the shear ratio. For a fixed value of the latter, the orientation of the fastest growing cells (the preferential cell direction) is nearly independent of the one other dimensionless parameter which could be the Stokes drift/friction velocity ratio or the Langmuir number. The direction of the fastest growing cells shifts closer toward the wave direction as the Stokes drift shear increases relative to the mean shear and vice versa. However, while the preferential cell direction lies close to the wind for small Sr, it does not align with the waves for reasonably large Sr. When wind and waves are not aligned and the Stokes drift shear and the mean shear are of the same order, the cells drift sideways at an angle to the cell axes, with a speed which is comparable with the magnitude of the mean Eulerian current at a depth of approximately 0.7 times the cell depth. The drift amplitude increases as the misalignment angle increases and is larger for larger values of the shear ratio. When wind and waves are oriented in the opposite directions, there is no source of instability, and the cells are damped. are parallel and predicts the formation of Langmuir cells aligned with both wind and waves [Leibovich, 1983]. Analysis of the observed surface structure of Langmuir circulation (V. Polonichko and D. Farmer, Observations of Langmuir circulation when wind and waves are misaligned, manuscript in preparation, 1997) under changing wind conditions indicates that the orientation of windrows is affected by the relative orientation of the surface Stokes drift and wind vectors. These observations motivate us to ask the following theoretical question: How does the relative Copyright 1997 by the American Geophysical Union. Paper number 97JC00466. 0148-0227/97/97 JC-00466509.00 orientation of the wind and the Stokes drift affect the orientation of Langmuir cells? Leibovich [1983] pointed out that such wind-wave misalignment might affect generation and structure of Langmuir cells, but Gnanadesikan and Weller [1995, p. 3161] (hereinafter referred to as GW) were the first to address this problem. They analyzed wave-current interaction within an Ekman layer of constant depth and concluded that one should expect cells to be generated in a direction, between the wind and the Stokes drift, "closer to the strongest shear." GW suggested that the growth rat...

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Section: The Reason That the Stokes Drift Is Less Effective In Alignisupporting

confidence: 77%

“…This result is, on the face of it, contradictory to Gnanadesikan [1996], who starts with a given wave height and a peak period and distributes it over a PM spectrum. The PM spectrum has a larger Sr and Su, which results in a larger growth rate.…”

Section: The Reason That the Stokes Drift Is Less Effective In Alignimentioning

confidence: 67%

Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift

Polonichko¹

1997

J. Geophys. Res.

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“…As for the vertical variation of w LC , it is reasonable that it is zero at the surface as well as at a finite depth H LC , which is often close to the mixed layer depth [ Skyllingstad and Denbo , 1995; Gnanadesikan and Weller , 1995; Gnanadesikan , 1996]. For reasons of simplicity it was assumed that The sine function was also suggested by the work of Gnanadesikan and Weller [1995] and Gnanadesikan [1996] as a first‐order profile for the Langmuir cell structures.…”

Section: Parameterization Of Langmuir Circulationsmentioning

confidence: 99%

Wind‐driven internal waves and Langmuir circulations in a numerical ocean model of the southern Baltic Sea

Axell

2002

J.Geophys.Res.

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[1] A one-dimensional numerical ocean model of the southern Baltic Sea is used to investigate suitable parameterizations of unresolved turbulence and compare with available observations. The turbulence model is a k-e model that includes extra source terms P IW and P LC of turbulent kinetic energy (TKE) due to unresolved, breaking internal waves and Langmuir circulations, respectively. As tides are negligible in the Baltic Sea, topographic generation of internal wave energy (IWE) is neglected. Instead, the energy for deepwater mixing in the Baltic Sea is provided by the wind. At each level the source term P IW is assumed to be related to a vertically integrated pool of IWE, E 0 , and the buoyancy frequency N at the same level, according toThis results in vertical profiles of e (the dissipation rate of TKE) and K h (the eddy diffusivity) according to e / N d and K h / N dÀ2 below the main pycnocline. Earlier observations are inconclusive as to the proper value of d, and here a range of values of d is tested in hundreds of 10-year simulations of the southern Baltic Sea. It is concluded that d = 1.0 ± 0.3 and that a mean energy flux density to the internal wave field of about (0.9 ± 0.3) Â 10 À3 W m À2 is needed to explain the observed salinity field. In addition, a simple wind-dependent formulation of the energy flux to the internal wave field is tested, which has some success in describing the short-and long-term variability of the deepwater turbulence. The model suggests that $16% of the energy supplied to the surface layer by the wind is used for deepwater mixing. Finally, it is also shown that Langmuir circulations are important to include when modeling the oceanic boundary layer. A simple parameterization of Langmuir circulations is tuned against large-eddy simulation data and verified for the Baltic Sea.INDEX TERMS: 4243 Oceanography: General: Marginal and semienclosed seas; 4544 Oceanography: Physical: Internal and inertial waves; 4572 Oceanography: Physical: Upper ocean processes; 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; KEYWORDS: Baltic Sea, mixing, turbulence model, Langmuir circulations, internal waves, internal wave energy Citation: Axell, L. B., Wind-driven internal waves and Langmuir circulations in a numerical ocean model of the southern Baltic Sea,

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“…Langmuir (1938) subsequently verified the existence of his proposed arrays of counter-rotating line vortices beneath the water surface with a series of observations in Lake George, New York. In the decades since his pioneering work, the circulations named after him have been studied by a variety of means, including laboratory studies (Faller & Caponi 1978), observations (Smith, Pinkel & Weller 1987;Zedel & Farmer 1991), theoretical studies (Craik & Leibovich 1976;Gnanadesikan 1996) and numerical modelling (Skyllingstad & Denbo 1995;McWilliams, Sullivan & Moeng 1997;Li, Garrett & Skyllingstad 2005). The papers cited here are a small selection from a large literature on the subject; further references are found within the text, and more complete coverage of the evolving literature can be found in reviews by Pollard (1976), Leibovich (1983) and Thorpe (2004).…”

Section: Introductionmentioning

confidence: 99%

Langmuir turbulence in shallow water. Part 1. Observations

Gargett

Wells

2007

J. Fluid Mech.

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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.

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Mixing driven by vertically variable forcing: an application to the case of Langmuir circulation

Cited by 11 publications

References 16 publications

Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift

Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift

Wind‐driven internal waves and Langmuir circulations in a numerical ocean model of the southern Baltic Sea

Langmuir turbulence in shallow water. Part 1. Observations

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