Asymptotic analysis of wavepackets in high speed boundary layers.

Analyzing the propagation of wavepackets in a boundary layer is useful in understanding laminar-turbulent transition phenomenon. In this work, a small amplitude coherent perturbation generates a wavepacket that is analyzed within the framework of Linear Stability Theory and the wavepacket comprised of coherent three dimensional disturbances is expressed as a double integral that is evaluated using asymptotic techniques. We demonstrate the application of the steepest descent method for wavepacket analysis valid at large downstream distances, while differing from currently published literature by accounting for a compressible, weakly non-parallel boundary layer. The steepest descent method identifies the wave frequency and wavenumber corresponding to the maximum amplitude of the wavepacket at an observation location and a Gaussian approximation around this maximum is used to construct the fine structures of the wavepacket. Details of wavepacket evolution in two high speed boundary layer perfect gas flows (edge Mach number, $M_e$=2 and $M_e$=7) over a flat plate at zero angle of attack are presented. Each case represents either Mack's first mode or second mode dominated flow instability.