# Espen Åkervik og Magnus Vartdal Forsvarets Forskningsinstitutt

Large Eddy Simulation of the interaction of water waves with turbulent air flow

The interaction of water waves and turbulent air flow is studied by means of Large Eddy Simulation, using both a one phase and a two phase formulation.

In the one phase formulation we seek to gain knowledge on how a simple propagating airy wave influences the turbulent boundary layer flow. In particular, we map out both the wave age dependence of the flow at a moderate friction Reynolds number of Re = 395. In addition, the Reynolds number dependence at the dynamically important wave age of c/u*=8. In line with previous work (cf Sullivan et al. 2000) we find that the form drag reaches a peak for young waves (c/u*<5) and becomes negative for old waves (c/u*>15). This implies that for swells, the interface acts as a supersmooth surface. Also in line with previous work is the critical layer dynamics, where the wave correlated shear stress switches sign at the critical layer. In terms of Reynolds number dependence, we find that the critical layer distance scales well in viscous units. We also find that the viscous distance from the wave crest is the relevant wall normal length scale for the turbulent stresses. As for channel flow, the streamwise peak rms scales as log(Re), however, with a larger growth factor.

The one phase approach fails to describe how the waves are affected by the turbulent wind. To gain insight in this, the wind-wave generation process is studied using a Volume of Fluid method. The coupled system is initiated by imposing a turbulent air flow on top of water at rest. Surface tension effects are excluded and the Froude number is chosen in order to fit young waves inside the computational domain. In the initial stage, the surface deformation consists of streamwise elongated narrow structures. These may be seen as footprints of the near wall streaks in the turbulent air flow. This phase is associated with linear growth in wave energy, and the behavior of the air flow is largely unaffected by the surface deformations. In the second stage, localized slow moving wave packets appear, and the air flow becomes linked to the wave motion, in close agreement with the Miles (1957) theory. This phase is associated with exponential growth of the waves. In the final stage of the simulation, non-linear interactions occur, resulting in redistribution of energy.