Editorial Type:
Article
Article Type:
Research Article

Toward a K-Profile Parameterization of Langmuir Turbulence in Shallow Coastal Shelves

Nityanand Sinha University of South Florida, Tampa, Florida

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Andres E. Tejada-Martínez University of South Florida, Tampa, Florida

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Cigdem Akan University of South Florida, Tampa, Florida

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Chester E. Grosch Ocean, Earth and Atmospheric Sciences, and Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, Virginia

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Print Publication:
01 Dec 2015
DOI:
https://doi.org/10.1175/JPO-D-14-0158.1
Page(s):
2869–2895
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Abstract

Interaction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law velocity profile, inducing a profile resembling a wake law. Furthermore, in the interior of the water column, two sources of Reynolds shear stress, turbulent (nonlocal) transport and local Stokes drift shear production, can combine to lead to negative mean velocity shear. Meanwhile, near the surface, Stokes drift shear serves to intensify small-scale eddies leading to enhanced vertical mixing and disruption of the surface log law. A K-profile parameterization (KPP) of the Reynolds shear stress comprising local and nonlocal components is introduced, capturing these basic mechanisms by which Langmuir turbulence in unstratified shallow water impacts the vertical mixing of momentum. Single-water-column, Reynolds-averaged Navier–Stokes simulations with the new parameterization are presented, showing good agreement with LES in terms of mean velocity. Results show that coefficients in the KPP may be parameterized based on attributes of the full-depth LC.

Corresponding author address: Andres E. Tejada-Martínez, Civil and Environmental Engineering, University of South Florida, 4202 E. Fowler Ave., ENB 118, Tampa, FL 33620. E-mail: aetejada@usf.edu

Abstract

Interaction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law velocity profile, inducing a profile resembling a wake law. Furthermore, in the interior of the water column, two sources of Reynolds shear stress, turbulent (nonlocal) transport and local Stokes drift shear production, can combine to lead to negative mean velocity shear. Meanwhile, near the surface, Stokes drift shear serves to intensify small-scale eddies leading to enhanced vertical mixing and disruption of the surface log law. A K-profile parameterization (KPP) of the Reynolds shear stress comprising local and nonlocal components is introduced, capturing these basic mechanisms by which Langmuir turbulence in unstratified shallow water impacts the vertical mixing of momentum. Single-water-column, Reynolds-averaged Navier–Stokes simulations with the new parameterization are presented, showing good agreement with LES in terms of mean velocity. Results show that coefficients in the KPP may be parameterized based on attributes of the full-depth LC.

Corresponding author address: Andres E. Tejada-Martínez, Civil and Environmental Engineering, University of South Florida, 4202 E. Fowler Ave., ENB 118, Tampa, FL 33620. E-mail: aetejada@usf.edu
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