Evaluation of the reduced Craik-Leibovich equations

Langmuir turbulence, engendered by the interaction of surface gravity waves and mean currents, drives various climatologically important mixing processes within the upper ocean and across the air-sea interface. The dynamics are well-described by the Craik-Leibovich (CL) equations, a wave-averaged version of the Navier--Stokes equations. Nevertheless, simulations of these equations in spatially extended domains remain computationally expensive. An asymptotic reduction of the CL equations termed the reduced CL (rCL) equations renders such simulations feasible by self-consistently filtering out small-scale downwind motions and exploiting the highly anisotropic dynamics that emerges in the strong surface-wave-forcing limit. In this investigation, we assess the accuracy and efficiency of simulations of the rCL equations via direct comparisons of computed flow structures and statistics with those obtained by simulating the full CL equations. Comparisons are made both within the formal regime of validity of the rCL equations, i.e. in the extreme wave-forcing limit, and outside it, with parameter values reflecting Langmuir turbulence in the presence of swell waves.