DIAGONALIZING APPROXIMATION FOR INHOMOGENEOUS TURBULENCE.
Research rept. no. 5
KRAICHNAN (ROBERT H) PETERBOROUGH N H
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An approximation for shear and Boussinesq turbulence was introduced which can greatly lessen the computational task associated with spatial inhomogeneity. It yields statistical equations for inhomogeneous flow which are of simplicity comparable to the direct-interaction equations for homogeneous flow. The new approximation presupposes a representation of the turbulent fields by expansion in some appropriate set of orthonormal functions which obey the boundary cpmditions. The covariances which are off-diagonal in the chosen representation, as well as the triple correlations, were approximated in terms of diagonal covariances and diagonal average response functions by a procedure resembling the direct-interaction scheme. The final equations involve only the mean-field amplitudes and the diagonal covariance and response functions. The approximation was illustrated by applying it to infinitePrandtl-number Boussinesq convection between infinite horizontal planes. The range of applicability and the limitations of the approximation were discussed. Author