Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Velikovich, A. L.; Schmit, P. F.

doi:10.1063/1.4938272

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Journal Article · Mon Dec 14 23:00:00 EST 2015 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4938272· OSTI ID:22489943

Velikovich, A. L. ^[1]; Schmit, P. F. ^[2]

Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375 (United States)
Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

OSTI ID:: 22489943

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 12 Vol. 22; ISSN PHPAEN; ISSN 1070-664X

Country of Publication:: United States

Language:: English

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