Models of Turbulent Airflow Above Idealised Water Waves

Abstract

In a series of papers Gent and Taylor (1976, 1977) and Gent (1977) have developed and applied a numerical model of deep turbulent boundary-layer flow above idealised, monochromatic, two dimensional water waves. The present paper will discuss some of their results and describe some recent developments to the model to study flow over differing shapes of wave. The Gent and Taylor model is essentially a numerical solution of the averaged continuity and Navier Stokes equations with closure hypotheses to relate second order correlations (the Reynolds stresses) to mean gradients via an isotropic eddy viscosity, K, which depends upon the local value of mean turbulent kinetic energy, E, and a mixing-length ℓ(z, z_O) which is prescribed as a function of position. It is a relatively simple closure scheme with few parameters. More complex higher order closure schemes or slightly different simple assumptions may be found to give better results but they preferred to use rather basic, simple closure hypotheses for their numerical experiments. Slightly different hypotheses were used by Townsend (1972) in his model of airflow over water waves which was linear in the waveslope (ak). Moderately good agreement between Gent and Taylor’s nonlinear model and Townsend’s results are reported for small values of ak (a is the amplitude and k the horizontal wavenumber).