A new boundary layer resonance enhanced by wave modulation: theory and experiment

When more than one wave is present in a system there exists the possibilty of a resonant interaction. Resonant modes become nonlinear at smaller amplitudes than nonresonant modes. If the nonlinearity causes increased growth rates then it may be that, for a time at least, the behaviour of the resonant modes will be the dominant feature. In shear layers resonant triads can be found where two oblique modes resonate with a plane wave and this case has received much attention in the literature. For a given plane wave, the resonance condition selects oblique modes of a certain wave angle and agreement has been found between predicted wave angles and those measured in experiments.

In this paper it is shown that resonance conditions can also be met between two planar waves in a Blasius boundary layer, where one of the waves is the usual unstable mode, and the other is a higher-order damped mode. The effects of wave modulation are modelled by performing a spatial analysis but allowing the frequency to become complex. It is found that for certain complex frequencies the strength of the nonlinear resonant interaction coefficients is greatly increased. Experiments have been performed in a low-turbulence wind tunnel in which disturbances with modulated and unmodulated sections were introduced into the boundary layer over a flat plate. It was found that disturbances with the frequency and modulation predicted by the theory do indeed show a much greater susceptibility to nonlinear breakdown than nonresonant disturbances.