University of Western Ontario
London, Ontario, Canada
We consider the nonlinear spatial evolution of a pair of varicose oblique waves together with a pair of sinuous oblique waves superimposed on a Bickley jet, with each wave being slightly amplified on a linear basis. The two pairs are assumed to both be inclined at the same angle to the plane of the jet. A nonequilibrium nonlinear critical layer analysis is employed to derive equations governing the evolution of the instability wave amplitudes, which contain a coupling between the modes. In the limit where one or the other of pairs of modes is absent, the equations reduce to the equation given by Goldstein and Choi (J. Fluid Mech. 207, 1989) for the evolution of a pair of oblique waves on a shear layer. We present numerical solutions of these amplitude equations and show that, as in related work for other problems, they may develop a singularity at a finite distance downstream.