Integro-differential closure equations for inhomogeneous turbulence

Abstract

We present numerical and computational techniques to solve systems of integro-differential closure equations for inhomogeneous two-dimensional turbulent flow. The closure equations, representing the first tractable closure theory for inhomogeneous flow over mean (single realization) topography, are based on a quasi-diagonal direct interaction approximation derived via renormalization techniques. The equations are computationally challenging due to the potentially long time history integrals. In order to reduce the computational cost we have implemented a formal restart procedure for the two and three point cumulant terms. The restart procedure is shown to be in good agreement with the closure without restarts and results are compared to direct numerical simulation of the barotropic vorticity equation.