Linear Stability of Self-Similar Flow: 1. Isothermal Cylindrical Implosion and Expansion.

Abstract : A soluble model of the development of the Rayleigh-Taylor instability in perturbations about a time-varying state of a compressible medium is presented. A Lagrangian description is employed to rederive the equations for the self-similar motion of an ideal fluid and to obtain the linearized equations of motion for perturbations about a general time-varying basic state. The resulting formalism is applied in cylindrical geometry to calculate the growth of flute-like Rayleigh-Taylor modes associated with a similarity solution modeling the implosion and expansion of a liquid liner. A complete solution is obtained for the perturbed motion. The only modes for which the perturbation amplitudes grow faster than the unperturbed linear radius are divergence- and curl-free. Numerical and analytical results are obtained for these and shown to reduce in the short wavelength limit to those previously for incompressible time-independent basic states. (Author)