Scaling and flow structure of Langmuir turbulence in inertial frames

Yun Chang aDept. of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA

Search for other papers by Yun Chang in
Current site
Google Scholar
PubMed
Close
and
Alberto Scotti bSchool for Engineering of Matter, Transport and Energy, ASU, Tempe, AZ

Search for other papers by Alberto Scotti in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

This paper provides a framework that unifies the characteristics of Langmuir turbulence, including the vortex force effect, velocity scalings, vertical flow structure, and crosswind spacing between surface streaks. The widely accepted CL2 mechanism is extended to explain the observed maximum alongwind velocity and downwelling velocity below the surface. Balancing the extended mechanism in the Craik-Leibovich equations, the scalings for the along-wind velocity u, cross-wind velocity v, and vertical velocity w are formulated as
U=UfLa2/3,V=W=(Uf2Us)1/3.
Here, Uf is the friction velocity, Us is the Stokes drift on the surface, and La = (Uf /Us)1/2 is the Langmuir number. Simulations using the Stratified Ocean Model with Adaptive Refinement in Large Eddy Simulation mode (LES-SOMAR) validate the scalings and reveal physical similarity for velocity and crosswind spacing. The horizontally averaged velocity along the wind ū/U on the surface grows with time, whereas v/V and w/W are confined. The root mean square (rms) of w peaks at wrms/W ≈ 0.85 at a depth of 1.3Zs, where Zs is the e-folding scale of the Stokes drift. The crosswind spacing L grows linearly with time but is finally limited by the depth of the water H, with maximum L/H = 3.3. This framework agrees with measurement collected in six different field campaigns.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yun Chang, yun.chang@whoi.edu

Abstract

This paper provides a framework that unifies the characteristics of Langmuir turbulence, including the vortex force effect, velocity scalings, vertical flow structure, and crosswind spacing between surface streaks. The widely accepted CL2 mechanism is extended to explain the observed maximum alongwind velocity and downwelling velocity below the surface. Balancing the extended mechanism in the Craik-Leibovich equations, the scalings for the along-wind velocity u, cross-wind velocity v, and vertical velocity w are formulated as
U=UfLa2/3,V=W=(Uf2Us)1/3.
Here, Uf is the friction velocity, Us is the Stokes drift on the surface, and La = (Uf /Us)1/2 is the Langmuir number. Simulations using the Stratified Ocean Model with Adaptive Refinement in Large Eddy Simulation mode (LES-SOMAR) validate the scalings and reveal physical similarity for velocity and crosswind spacing. The horizontally averaged velocity along the wind ū/U on the surface grows with time, whereas v/V and w/W are confined. The root mean square (rms) of w peaks at wrms/W ≈ 0.85 at a depth of 1.3Zs, where Zs is the e-folding scale of the Stokes drift. The crosswind spacing L grows linearly with time but is finally limited by the depth of the water H, with maximum L/H = 3.3. This framework agrees with measurement collected in six different field campaigns.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yun Chang, yun.chang@whoi.edu
Save