The initial-value problem for the Kelvin-Helmholtz instabilities of high-velocity and magnetized shear layers

The general initial-value problem for the Linear Kelvin-Helmholtz instability of arbitrarily compressible velocity shear layers is considered for both the unmagnetized and magnetized cases. The time evolution of the physical quantities characterizing the layer is treated using Laplace transform techniques. Singularity analysis of the resulting equations using Fuchs-Frobenius theory yields the large-time asymptotic solutions. The instability is found to remain, within the linear theory, of the translationally convective or shear type. No onset of rotational or vortex motion, i.e., formation of ''coherent structures'' occurs.