Predicting Second-Mode Instability Evolution in Hypersonic Boundary Layers Using Machine Learning Methods

The growth and breakdown of second-mode instability in hypersonic boundary layers are commonly characterized by analyzing surface pressure spectra. For the hypersonic boundary layer over a sharp cone, this study predicts the spectral evolution of instability waves at the downstream and upstream targets based on the multiple input locations, namely, the forward and inverse models. Based on spectral information of four upstream locations, the forward model can capture the growth and disappearance of spectral peaks associated with the second-mode instability, showing that the relative amplitude is captured within 20% error at all flow conditions. Similarly, the inverse model can accurately describe the spectral distribution of instability waves at the upstream location, providing the onset and peak frequency with less than 10% error. Besides, the iterated forward model captures the disappearance of the dominant spectral peak for [Formula: see text], suggesting the availability of spatial prediction by only three input locations. Moreover, the model training process evaluates the relative importance of each input variable. The feature importance profiles indicate the nearest location’s dominant role but prove that spatial dependence does not solely decrease with distance. While the current paper focused on the hypersonic boundary layer over a sharp cone at Mach 6 at a 0 deg angle of attack, the approach of prediction beyond the measurement region using data-driven methods has broader potential. Extending these methods could provide a robust framework for predicting and understanding transition processes in various flow conditions.