## JMI2009B-5 Algebraic instability caused by acoustic modes in supersonic shear flows (pp.123-130)

Author(s)： Makoto Hirota and Zensho Yoshida

J. Math-for-Ind. **1B** (2009) 123-130.

- File： JMI2009B-5.pdf (303KB)

Abstract

Perturbations in a shear flow exhibit rather complex behavior -- waves may grow algebraically even when the spectrum of disturbances is entirely neutral (no exponential instability). A shear flow brings about non-selfadjoint property, invalidating the standard notion of dispersion relations, and it also produces a continuous spectrum that is a characteristic entity in an infinite-dimension phase space. This paper solves an initial value problem using the Laplace transform and presents a new-type of algebraic instability that is caused by resonant interaction between acoustic modes (point spectrum) and vortical continuum mode (continuous spectrum). Such a resonance is possible when variation of velocity shear is comparable to sound speed.

Keyword(s). compressible fluid, shear flow, spectrum of non-selfadjoint operator, algebraic instability