Simulation and Theoretical Modeling of Interactions between Waves and Turbulence in Langmuir Circulation

Abstract

Langmuir turbulence arising from the interaction of turbulence with surface waves can significantly change the transport and mixing in the oceanic surface layer. Previously, Langmuir turbulence has been studied extensively using the wave-phase-averaged Craik–Leibovich (CL) equations, which average turbulent motions over timescales comparable to or shorter than the wave period and model the accumulative wave effect. However, our understanding of the turbulent processes within a wave period is still incomplete, and thus, the validity and accuracy of the CL model remain unclear. In the present work, we use a wave-phase-resolved large-eddy simulation (LES) to study the wave–turbulence interaction processes directly without the CL modeling approximation. For the first time, the detailed wave-phase modulation of the vortex structures and Reynolds stresses in Langmuir turbulence is revealed. To implement the wave-phase-resolved LES, a numerical scheme with good conservation properties and accuracy is developed using a wave-surface-fitted curvilinear grid. Simulations are carried out for the canonical set-up of the Langmuir turbulence beneath a monochromatic wave with steady and co-aligned wind-driven surface stress. Analyses of the turbulence statistics show that the vortex structures and the intensity of the turbulent fluctuations depend on the wave phase. The mechanisms underlying the correlation of the turbulence statistics with the wave phase are also investigated through analyses of the vorticity transport equations and Reynolds stress budgets. Straining induced by wave orbital motions plays an important role in the wave-phase variation of these quantities. The accumulative wave effect on turbulence is examined by the Lagrangian average of the transport equations. It is discovered that the correlations between turbulence and wave orbital straining can contribute to the wave-phase-averaged evolution of the vorticity and turbulent kinetic energy. Models are proposed for the vorticity distortion by waves and energy transfer from waves to turbulence. Overall, our findings indicate that fast turbulent fluctuations near the wave frequency are important for the wave–turbulence interaction. The effect related to these wave-phase correlated fluctuations is not fully resolved by the CL model. This thesis constitutes an important step towards the improved modeling of Langmuir turbulence.