Soluble model for the analysis of stability in an imploding compressible liner

Journal Article · Mon Jan 01 00:00:00 EST 1979 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.862437· OSTI ID:6462012

Book, D L; Bernstein, I B

A soluble model of the development of the linear pertubations 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 pertubations about a general time-varying basic state. The resulting formalism is applied in cylindrical geometry to calculate the growth of flute-like modes associated with a similarity solution modeling the implosion and expansion of a fluid liner. A complete solution is obtained for the perturbed motion. The only modes for which the perturbation amplitudes grow faster than the unperturbed liner radius during both implosion and expansion are divergence- and curl-free. Numerical and analytical results are obtained for these and shown to reduce, in the short-wavelength limit, to the Rayleigh--Taylor instability found previously for incompressible time-independent basic states. In addition, a new kind of instability is found: a class of overstable internal modes (sound waves), which are ''pumped up'' in amplitude during implosion, but decay during the expansion phase.

• Research Organization: Laboratory for Computational Physics, U. S. Naval Research Laboratory, Washington, D. C. 20375
• OSTI ID: 6462012
• Journal Information: Phys. Fluids; (United States), Vol. 22:1
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
LINERS
IMPLOSIONS
LIQUID METALS
BOUNDARY CONDITIONS
CYLINDRICAL CONFIGURATION
DISTURBANCES
EQUATIONS OF MOTION
FLUTE INSTABILITY
IDEAL FLOW
LAGRANGIAN FUNCTION
LINUS REACTORS
RAYLEIGH-TAYLOR INSTABILITY
CONFIGURATION
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
FLUID FLOW
FLUIDS
FUNCTIONS
INSTABILITY
LIQUIDS
METALS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
THERMONUCLEAR REACTORS
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