Numerical simulations of `pure' Langmuir turbulence

Langmuir turbulence, engendered by the interaction of surface gravity waves and mean Eulerian currents, is a prominent upper ocean mixing process. A coarse-grained description of this phenomenon is provided by the reduced Craik-Leibovich (rCL) equations, which can be derived via multiple-scales asymptotic analysis of the governing Craik-Leibovich (CL) equations in the strong CL vortex-force limit. The rCL equations self-consistently suppress nonlinear advection by the (Eulerian) downwind velocity and, thus, the mechanisms responsible for the sustenance of shear-flow turbulence in the extit{absence} of waves. Crucially, the rCL equations also obviate the need to temporally resolve rapid-distortion transients driven by the wave Stokes drift, in principle facilitating simulation of Langmuir turbulence over long times and in spatially extended domains. Unfortunately, prior simulations of the rCL equations in this `pure' Langmuir turbulence regime have been stymied by the occurrence of spurious cross-wind banding in the downwind velocity field. In this work, we resolve this issue and characterize rCL dynamics in the pure Langmuir turbulence regime, highlighting a 2:1 spatial resonance that dominates surface patterning.