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Velocity-Vorticity Decomposition of the Reynolds Stress Gradient in a Shear Layer

Scott C. Morris
Department of Aerospace and Mechanical Engineering University of Notre Dame 110 Hessert Laboratory, Notre Dame, IN 46556 USA

John F. Foss
Department of Mechanical Engineering Michigan State University East Lansing, Ml 48824 USA

Aren M. Hellum
Department of Mechanical Engineering Michigan State University East Lansing, Ml 48824 USA

Resumo

Time series measurments of velocity and vorticity using a four sensor hot-wire technique have been acquired in a large scale single stream shear layer. The Reynolds stress gradient which appears in the time averaged momentum equation can be written in terms of the velocity-vorticity products. The experimental data allows for the evaluation of these quantities, and the spectral content of the time series provides insight into the scales of motion which lead to the time averaged values.
The power spectral density function for the vorticity time series (ωz, ωy) show substantial values at a wide range of wave numbers. The velocity-vorticity products also indicates a wide distribution in wave number space. This indicates the existence of anisotropic motions which contribute to the Reynolds shear stress gradient at wave numbers at both very high and very low wave numbers.