A Wave-Resolving Simulation of Langmuir Circulations with a Nonhydrostatic Free-Surface Model: Comparison with Craik–Leibovich Theory and an Alternative Eulerian View of the Driving Mechanism

The present study performs a wave-resolving simulation of wind-driven currents under monochromatic surface gravity waves using the latest nonhydrostatic free-surface numerical model. Here, phase speed of the waves is set much greater than the current speed. Roll structures very similar to observed Langmuir circulations (LCs) appear in the simulation only when both waves and down-wave surface currents are present, demonstrating that the rolls are driven by the wave–current interaction. A vorticity analysis of simulated mean flow reveals that the rolls are driven by the torque associated with wave motion, which arises from a correlation between wave-induced vorticity fluctuation and the wave motion itself. Furthermore, it is confirmed that the wave-induced torque is very well represented by the curl of the vortex force (VF), that is, the vector product of mean vorticity and Stokes drift velocity. Therefore, it is concluded that the simulated rolls are LCs and that the wave effects are well represented by the VF expression in the present simulation. The present study further revisits the scaling assumptions made by previous studies that derived VF formulation and shows that there is disagreement among the previous studies regarding the applicability of VF formulation when the wave orbital velocity (proportional to the amplitude times the frequency) is much smaller than the mean flow velocity. The result from the present simulation shows that the VF expression is still valid even with such small wave amplitudes, as long as phase speed of the waves is much greater than the current speed.