A tractable inhomogeneous closure theory for flow over mean topography

Abstract

The quasi-diagonal direct interaction approximation (QDIA) is shown to be a computationally tractable closure theory for inhomogeneous two-dimensional turbulent flow over mean (single-realization) topography. In this paper numerical results for the QDIA are compared to direct numerical simulation (DNS) at moderate Reynolds number for two cases with quite different topographic and mean field amplitudes. The QDIA is found to be in excellent agreement with DNS for cases where the small-scale topographic amplitude is significant. For cases where the small-scale topography is weak, the QDIA closely reproduces the evolving mean field and large-scale energy containing transients but under represents the amplitudes of the small-scale transients in a similar way to the homogeneous DIA. We discuss the prospects of ameliorating the small-scale deficiencies using a regularization of the interaction coefficients.