Nonlinear Stability of a Mach 1.6 Flat Plate Boundary Layer

Abstract

Nonlinear stability and transition mechanisms for a Mach 1.6 flat-plate boundary layer are examined by numerically solving the governing partial differential equations. It is shown that subharmonic secondary instability mechanism for a two-dimensional primary disturbance requires initial amplitude on the order of about.5% for the primary wave. When both two-and three-dimensional waves have an initial amplitude of.1%, transition is associated with the breakdown of oblique first-mode waves. This oblique-mode breakdown process involves two stages. First, nonlinear interaction of a pair of oblique waves with equal but opposite angles results in the evolution of a wave-vortex triad consisting of the oblique waves and a streamwise vortex whereby the oblique waves grow linearly while nonlinear forcing results in the rapid growth of the vortex mode. In the second stage, when the wave-vortex triad reaches sufficiently large amplitudes, secondary instability associated with the interaction of the oblique waves and the vortex takes place. This secondary instability eventually triggers rapid growth of other harmonic waves and transition soon follows.