Abstract

We present numerical and computational techniques to solve systems of integro-differential closure equations for inhomogeous 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 complexity of the closure equations also requires a sophisticated use of predictor-corrector (forward time step) and trapezoidal (integrals) methods as well as prudent storage of the interaction coefficients. The restart procedure is shown to be in good agreement with the closure and results are compared to direct numerical simulation of the barotropic vorticity equation.

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