Analytic theory of Richtmyer{endash}Meshkov instability for the case of reflected rarefaction wave

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.868938· OSTI ID:284280

Velikovich, A L ^[1]

---

1. Berkeley Scholars, Inc., Springfield, Virginia 22150 (United States)

An analytic theory of the Richtmyer{endash}Meshkov (RM) instability for the case of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a {open_quote}{open_quote}stand-alone{close_quote}{close_quote} rarefaction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration of the interface. This confirms that the RM instability is not caused by the instant normal acceleration of the interface, and hence, is not a type of Rayleigh{endash}Taylor instability. The RM instability is related to the growth of initial transverse velocity perturbations at the interface, which may be either present initially as in symmetrical Riemann problem, or be induced by a shock passing a corrugated interface. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 284280
• Journal Information: Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 6 Vol. 8; ISSN 1070-6631; ISSN PHFLE6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMPRESSIBILITY
FLUID-FLUID INTERFACES
GAS FLOW
INSTABILITY
PERTURBATION THEORY
SHOCK WAVES