Nonlinear shear-layer instability waves

The effects of critical-layer nonlinearity on spatially growing instability waves on shear layers between parallel streams are discussed. In the two-dimensional incompressible case, the flow in the critical layer is governed by a nonequilibrium (unsteady) nonlinear vorticity equation. The initial exponential growth of the instability wave is converted into algebraic growth during the streamwise aging of the critical layer into a quasi-equilibrium state. A uniformly valid composite formula for the instability wave amplitude, accounting for both nonparallel and nonlinear effects, is shown to be in good agreement with available experimental results. Nonlinear effects occur at smaller amplitudes for the three-dimensional and supersonic cases than in the two-dimensional incompressible case. The instability-wave amplitude evolution is then described by one integro-differential equation with a cubic-type nonlinearity, whose inviscid solution always end in a singularity at finite downstream distance.The US Government has the right to retain a nonexclusive royalty-free license in and to any copyright covering this paper.