Directly Simulated Wave-Current Mutual Interaction: Surface Wave Modulation Intensifies Langmuir Circulations

Langmuir circulations are considered to be driven by surface waves’ residual effect on underlying current. To simulate such an effect, the Craik-Leibovich (CL) equation is widely used, where the waves’ effect on the current is represented using prescribed Stokes drift profile, and waves are assumed to be unaffected by the current.

In this study, wave-resolving direct numerical simulations of Langmuir circulations in idealized configurations are conducted to explore currents’ effect on waves and its possible impact on Langmuir circulations. Simulations with the CL equation are also conducted for comparative study. To explicitly simulate surface wave motions and underlying current at the same time, a newly developed curvilinear-coordinate free surface numerical model is used.

Simulation results show that the CL simulations tend to underestimate the intensity of large Langmuir cells (ones with a horizontal scale larger than the wavelength). The waves become modulated in the spanwise direction due to a refraction-like response to the down-wind jet associated with Langmuir circulations, leading to horizontally sheared Stokes drift. Vorticity budget analysis reveals that the horizontal shear in Stokes drift tilts the spanwise vorticity associated with wind-driven shear to intensify the Langmuir cells.