Buoyancy instability of homologous implosions
With this study, I consider the hydrodynamic stability of imploding ideal gases as an idealized model for inertial confinement fusion capsules, sonoluminescent bubbles and the gravitational collapse of astrophysical gases. For oblate modes (short-wavelength incompressive modes elongated in the direction of the mean flow), a second-order ordinary differential equation is derived that can be used to assess the stability of any time-dependent flow with planar, cylindrical or spherical symmetry. Upon further restricting the analysis to homologous flows, it is shown that a monatomic gas is governed by the Schwarzschild criterion for buoyant stability. Under buoyantly unstable conditions, both entropy and vorticity fluctuations experience power-law growth in time, with a growth rate that depends upon mean flow gradients and, in the absence of dissipative effects, is independent of mode number. If the flow accelerates throughout the implosion, oblate modes amplify by a factor (2C)^{|N0|ti}, where C is the convergence ratio of the implosion, N_{0} is the initial buoyancy frequency and t_{i} is the implosion time scale. If, instead, the implosion consists of a coasting phase followed by stagnation, oblate modes amplify by a factor exp(π|N_{0}|t_{s}), where N_{0} is the buoyancy frequency at stagnation and t_{s} is the stagnation time scale. Evenmore »
- Publication Date:
- OSTI Identifier:
- 1251085
- Report Number(s):
- LLNL-JRNL--671017
Journal ID: ISSN 0022-1120; applab
- Grant/Contract Number:
- AC52-07NA27344
- Type:
- Accepted Manuscript
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 774; Journal Issue: 06; Journal ID: ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Research Org:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org:
- USDOE
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS compressible flows; instability; sonoluminescence