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| Langmuir circulation (LC) is a convective flow in the ocean surface mixed layer characterized by an array of wind-aligned, counter-rotating vortices. The vortex system arises as an instability of a vertically-sheared current on which high-frequency surface gravity waves propagate. By filtering these waves, the Craik--Leibovich (CL) equations facilitate investigation of LC, but numerical simulations of the fully three-dimensional (3D) CL equations in spatially-extended domains nevertheless require immense computing resources. Here, an asymptotically-reduced version of the CL equations -- the rCL equations -- is presented. The rCL equations render numerical simulations in very long (streamwise) domains more feasible by exploiting the strongly anisotropic structure of LC that emerges in the physically-relevant limit of strong surface-wave forcing. Linear and secondary stability analyses as well as pseudospectral nonlinear simulations of the rCL equations confirm that they capture dynamics reminiscent of LC. A novel 2:1 spatial resonance phenomenon, mediated by downwind variability of the convective flow, is shown to be a robust feature of the reduced dynamics. This 2:1 resonance is captured in its most pristine form in a numerically exact, steady 3D traveling wave solution of the rCL equations. The associated Lagrangian surface patterns reveal the presence of Y-junctions preferentially oriented downwind, as is commonly reported in field observations of LC. |
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