ON THE FINITE-AMPLITUDE DEVELOPMENT OF NEAR-SINGULAR MODES OF THE BICKLEY JET

GORDON E. SWATERS

Abstract. The linear stability spectrum of the Bickley jet has neutral modes which have a phase velocity equal to the maximum jet velocity. Previous numerical simulations initialized with a monochromatic near-singular mode with a nonzero phase shift across the critical levels have shown that there is a slow time oscillation in the transverse transport of perturbation energy in which the energy flux goes from one critical level to the other and then reverses and so on, all the while satisfying no net energy transfer from the mean flow to the perturbation field. Weakly nonlinear asymptotics suggests that higher harmonics are generated in the critical layer. However, previous numerical simulations do not seem to suggest the development of these modes. Here we examine numerically the evolution of these higher harmonics by initializing a simulation with them explicitly present.