A combined VOF-RANS approach for studying the evolution of incipient wind-generated waves over a viscous liquid

Recent laboratory experiments have revealed that important insights into the physical processes involved in the wind-driven generation of surface waves may be obtained by varying the viscosity of the carrying liquid over several orders of magnitude. The present paper reports on the development of a companion approach aimed at studying similar phenomena through numerical simulation. After reviewing available options, we select and approach based on the combination of a volume of fluid technique to track the evolution of the air-liquid interface, and a two-dimensional Reynolds-averaged version of the Navier-Stokes equations supplemented with a turbulence model to predict the velocity and pressure fields in both fluids. We examine the formal and physical frameworks in which such a formulation is meaningful, and close the governing momentum equations with the one-equation Spalart-Allmaras model which directly solves a transport equation for the eddy viscosity. For this purpose, we assume the interface to behave as a rigid wall with respect to turbulent fluctuations in the air, and implement a versatile algorithm to compute the local distance to the interface whatever its shape. We first assess the performance of this model in the single-phase configuration of flow over a wavy rigid wall, which is of specific relevance with respect to wind-wave generation. Then, we discuss the initialization protocol used in two-phase simulations, which involves a white noise distribution applied to the interface position. We finally present some examples of interface evolutions obtained at several wind speeds with liquids of various viscosities.