Nonlinear development and secondary instability of largeamplitude Goertler vortices in hypersonic boundary layers
Abstract
A weakly nonlinear theory is presented for investigating the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position and for deriving two coupled evolution equations. The latter makes it possible to determine whether the vortices are decaying or growing depending on the sign of a controlling constant. It is found that if the vortices are growing, the mean flow correction becomes so large as to affect the basic state of distances downstream of the neutral position. A fully nonlinear theory concerning the further downstream development of these largeamplitude Goertler vortices is also presented. The upper and lower boundaries of the region of vortex activity are determined by a freeboundary problem involving the boundary layer equations. Attention is also given to the secondary instability of the flow in the transition layers centered at the upper and lower boundaries of the region of vortex activity. It is found that the superimposed perturbations are spanwise periodic traveling waves, which are pi/2 radians out of phase with the fundamental.
 Publication:

European Journal of Mechanics, B/Fluids
 Pub Date:
 1991
 Bibcode:
 1991EuJMB..10..283F
 Keywords:

 Goertler Instability;
 Hypersonic Boundary Layer;
 Nonlinear Equations;
 Vortices;
 Boundary Layer Equations;
 Traveling Waves;
 Turbulent Boundary Layer;
 Fluid Mechanics and Heat Transfer