Direct Numerical Simulation of Surface Waves and Turbulent Boundary Layer Interaction*

Wind-wave interaction happens when the wind blows across the surface water waves. The waves grow under the wind forcing, and at the same time, alter the turbulent boundary layer above them. The dynamics of this common but complex phenomenon is a long-standing problem that attracts both theoretical and practical interests. To seek a better physical understanding of this two-way coupling between wind and waves, we conduct direct numerical simulations of the two-phase Navier-Stokes equations with adaptive mesh refinement (AMR). A turbulent boundary layer flow interacts with a traveling wave train in a fully coupled manner, without any prescribed interfacial conditions. We explore a range of controlling parameters including wave age (ratio of wave speed and friction velocity) and wave slope. We analyze the dynamics of the turbulent air and water flow, as well as the wave growth. We also report the momentum and energy budgets, focusing on the pressure and shear stress partition. Such high fidelity simulations of the fully coupled wind-wave problem aim to improve the parameterization of the wind energy input term for wave growth, as well as provide references for the development of LES models of the marine atmospheric boundary layer that include surface wave effects.