Kinetic energy of Rayleigh--Taylor and Richtmyer--Meshkov instabilities

Journal Article · Thu Oct 31 23:00:00 EST 1991 · Physics of Fluids A; (United States)

DOI:https://doi.org/10.1063/1.858151· OSTI ID:5232970

Mikaelian, K O ^[1]

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1. University of California, Lawrence Livermore National Laboratory, Livermore, California (USA)

General expressions for the kinetic energy associated with Rayleigh--Taylor (RT) and Richtmyer--Meshkov (RM) instabilities in incompressible fluids are derived. The results are valid for small perturbations in continuous as well as discontinuous density profiles. It was found that KE{sup RT} /KE{sup RM}={ital ge}{sup 2{gamma}{tau}} /({Delta}{ital v}{Gamma}){sup 2}=({ital ge}{sup {gamma}{tau}}/{Delta}{ital v}{gamma}){sup 2}, where {tau}=time, {ital g}=acceleration, {Delta}{ital v}=velocity jump, and {gamma} is the exponential growth rate of the RT amplitude. The linear growth rate of the RM amplitude is {Delta}{ital v}{Gamma}{sup 2}={Delta}{ital v}{gamma}{sup 2}/{ital g}, and is found by solving an eigenvalue equation for a given density profile subject to appropriate boundary conditions. In general, KE{sup RT} asymptotes to a constant value at large {ital k} ({ital k}=2{pi}/{lambda}, {lambda}=wavelength), while KE{sup RM} continues to grow with {ital k}. Several analytic examples are illustrated and the {ital k} dependence of the kinetic energies is displayed.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5232970
• Journal Information: Physics of Fluids A; (United States), Journal Name: Physics of Fluids A; (United States) Vol. 3:11; ISSN 0899-8213; ISSN PFADE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
DENSITY
EIGENVALUES
ENERGY
ERUPTIVE VARIABLE STARS
FLUID FLOW
ICF DEVICES
INCOMPRESSIBLE FLOW
INSTABILITY
INSTABILITY GROWTH RATES
KINETIC ENERGY
PERTURBATION THEORY
PHYSICAL PROPERTIES
RAYLEIGH-TAYLOR INSTABILITY
STARS
SUPERNOVAE
THERMONUCLEAR DEVICES
VARIABLE STARS
WAVE PROPAGATION