Soluble model for the analysis of stability in an imploding compressible liner
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
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Related Subjects
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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640420 - Fluid Physics- Properties & Structure of Fluids- (-1987)