# The Initial Value Problem for the Kelvin-Helmholtz Instabilities of Compressible, Magnetized Tangential Velocity Discontinuities with Generalized Polytrope Laws

## Document Type

Article

## Publication Date

2002

## Abstract

The general initial-value problem for the linear Kelvin-Helmholtz instability of arbitrarily compressible magnetized anisotropic velocity shear layers is considered. 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. Since all the singular points turned out to be real, the instability is found to remain, within the linear theory, of the translationally convective shear type. No onset of rotational or vortex motion, i.e., formation of "coherent structures" occurs because there are no imaginary singularities.

## Recommended Citation

Kevin G. Brown and S. Roy Choudhury, The Initial Value Problem for the Kelvin-Helmholtz Instabilities of Compressible, Magnetized Tangential Velocity Discontinuities with Generalized Polytrope Laws, Quarterly of Applied Mathematics, LX, 4, 657-673, (2002).