Scaling and flow structure of Langmuir turbulence in inertial frames

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 alongwind velocity u, crosswind velocity υ, and vertical velocity w are formulated as U = UfLa^(2/3) and V = W = (Uf^2 Us)^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 (LES-SOMAR) mode validate the scalings and reveal physical similarity for velocity and crosswind spacing. The horizontally averaged velocity along the wind u/U on the surface grows with time, whereas υ/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 Lp grows linearly with time but is finally limited by the depth of the water H, with maximum Lp/H = 3.3. This framework agrees with measurement collected in six different field campaigns.