Langmuir turbulence in the ocean

TLDR

Large‑eddy simulations of phase‑averaged equations for the surface planetary boundary layer include terms proportional to the Lagrangian Stokes drift, and the turbulent Langmuir number La_tur = (U*/Us)^1/2 quantifies the relative influence of wind‑driven shear and Stokes drift. The study investigates equilibrium solutions for a wind‑driven PBL with steady, aligned wind and waves at a realistic turbulent Langmuir number La_tur = 0.3. The authors analyze large‑eddy simulation solutions of the phase‑averaged equations for the surface PBL, incorporating vortex, Coriolis, and tracer‑advection terms proportional to the Stokes drift. The simulations reveal that, at La_tur = 0.3, the mean current transports volume to the right of the wind and against the Stokes drift, while Stokes drift enhances turbulent momentum and tracer fluxes, kinetic energy, dissipation, and vertical‑velocity skewness; the dominant coherent structure is a Langmuir cell with longitudinal vorticity that intensifies near the surface, expands with depth, and exhibits irregular, finite‑scale patterns that merge at Y‑junctions.

Abstract

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, La tur = ( U ∗/ U s ) 1/2 , measures the relative influences of directly wind-driven shear (with friction velocity U ∗) and the Stokes drift U s . We focus on equilibrium solutions with steady, aligned wind and waves and a realistic La tur = 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.