Bursting frequency predictions for compressible turbulent boundary layers

Abstract

A computational method for the prediction of the bursting frequency associated with the coherent streamwise structures in high-speed compressible turbulent boundary layers is presented. The structures are described as wavelike disturbances of the turbulent mean flow. A direct resonance theory is used to determine the frequency of bursting. The resulting hydrodynamic linear stability equations are discretized by using a Chebyshev collocation method. A global numerical method capable of resolving the entire eigenvalue spectrum is used. Realistic turbulent mean velocity and temperature profiles are applied. For all of the compressible turbulent boundary layers calculated, the results show at least one frequency that satisfies the resonance condition. A second frequency can be identified for cases with high Reynolds numbers. An estimate is also made for the profile distribution of the temperature disturbance.