OBLIQUE-MODE BREAKDOWN AND SECONDARY INSTABILITY IN SUPERSONIC BOUNDARY-LAYERS

Laminar-turbulent transition mechanisms for a supersonic boundary laye r are examined by numerically solving the governing partial differenti al equations. It is shown that the dominant mechanism for transition a t low supersonic Mach numbers is associated with the breakdown of obli que first-mode waves. The first stage in this breakdown process involv es nonlinear interaction of a pair of oblique waves with equal but opp osite angles resulting in the evolution of a streamwise vortex. This s tage can be described by 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 mod e. In the second stage, the mutual and self-interaction of the streamw ise vortex and the oblique modes results in the rapid growth of other harmonic waves and transition soon follows. Our calculations are carri ed all the way into the transition region which is characterized by ra pid spectrum broadening, localized (unsteady) flow separation and the emergence of small-scale streamwise structures. The r.m.s. amplitude o f the streamwise velocity component is found to be on the order of 4-5 % at the transition onset location marked by the rise in mean wall she ar. When the boundary-layer flow is initially forced with multiple (fr equency) oblique modes, transition occurs earlier than for a single (f requency) pair of oblique modes. Depending upon the disturbance freque ncies, the oblique mode breakdown can occur for very low initial distu rbance amplitudes (on the order of 0.001% or even lower) near the lowe r branch. In contrast, the subharmonic secondary instability mechanism for a two-dimensional primary disturbance requires an initial amplitu de on the order of about 0.5% for the primary wave. An in-depth discus sion of the oblique-mode breakdown as well as the secondary instabilit y mechanism (both subharmonic and fundamental) is given for a Mach 1.6 flat-plate boundary layer.