A wave-guide model for turbulent shear flow

Abstract

It is shown that for a dynamical system admitting wave propagation modes (i.e. a wave-guide) the cross-power spectral density for stationary random fluctuations in the system will be dominated by the waves if they are lightly damped, the reason being that these can correlate over large distances of the order the inverse of the damping ratio. For a turbulent shear flow the wave propagation constant is obtained approximately from the solution of the Orr-Sommerfeld problem for the mean flow. Numerical calculations for a flat-plate boundary layer produce results for the streamwise dependence of the cross-power spectral density for the surface pressure fluctuations in good qualitative and quantitative agreement with measurements. An exception is the convection velocity for which the theory predicts a value that is somewhat too low.