Novel dynamics in the nonlinear evolution of the Kelvin-Helmholtz instability of supersonic anisotropic tangential velocity discontinuities

A nonlinear stability analysis using a multiple-scales perturbation procedu re is performed for the instability of two layers of immiscible, strongly a nisotropic, magnetized, inviscid, arbitrarily compressible fluids in relati ve motion. Such configurations are of relevance in a variety of astrophysic al and space configurations. For modes near the critical point of the linea r neutral curve, the nonlinear evolution of the amplitude of the linear fie lds on the slow first-order scales is shown to be governed by a complicated nonlinear Klein-Gordon equation. The nonlinear coefficient turns out to be complex, which is, to the best of our knowledge, unlike previously conside red cases and leads to completely different dynamics from that reported ear lier. Both the spatially-dependent and space-independent versions of this e quation are considered to obtain the regimes of physical parameter space wh ere the linearly unstable solutions either evolve to final permanent envelo pe wave patterns resembling the ensembles of interacting vortices observed empirically, or are disrupted via nonlinear modulation instability. In part icular, the complex nonlinearity allows the existence of quasi-periodic and chaotic wave envelopes, unlike in earlier physical models governed by nonl inear Klein-Gordon equations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.