Nonlinear instability of viscous modes in hypersonic flow past a wedge

The weakly nonlinear stability of a compressible flow past a wedge with an attached shock is investigated in the hypersonic limit. Interest is focused on Tollmien-Schlichting waves governed by a triple-deck structure and it is found that the attached shock, which occurs in the uppermost tier of the triple deck, can profoundly affect the stability characteristics of the flow. It is shown that nonlinearity tends to have a stabilizing influence on the flow and the nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits. These results are compared with those for the shock-free problem.