Eddy viscosity of cellular flows by upscaling
The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ??0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational investigation of eddy viscosity, when the small-scale flows are cellular, special periodic stationary flows with the stream function ?=siny1siny2+?cosy1cosy2, y=x/?, 0???1. For small ? we used a numerical upscaling method. We designed this method so that it captures the modulational perturbations for any ? with O(?2) accuracy and independent of ? complexity.
eddy viscosity upscaling computational fluid dynamics