AN EFFICIENT METHOD FOR INVESTIGATING THE FLOW EVOLUTION IN SHEAR LAYERS

This paper uses the 'natural' method proposed by Vallis et al. (1989) to determine stable flow configurations and investigates the inviscid dynamics of the barotropic shear-layer with a hyperbolic tangent veloc ity profile in a channel. The 'modified' dynamics provides a simplifie d picture of the flow transitions not marred by small scale vorticity oscillations found in the 'actual' dynamics. The transitions to quasi- steady or steady-states are characterized in physical space by vortex pairing and the final stable state is a single Vortex occupying the en tire channel length if the initial conditions allow an even wavenumber to dominate. Otherwise, when an odd wavenumber grows, the final state is constrained by higher order vorticity invariants and does not quit e fill the channel. For initial conditions favoring even wavenumbers, single wave quasi-steady states tend to agree with nonlinear analytica l predictions. The modified dynamics does well at capturing these stat es.