BellPlesset effects in RayleighTaylor instability of finitethickness spherical and cylindrical shells
BellPlesset (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 RayleighTaylor instability in radiationdriven spherical capsules and magneticallydriven 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 finitethickness shells through acceleration and deceleration phases. The timedependent 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 efoldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thinshell perturbationequations and approximate thinshell 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)].
 Authors:

^{[1]}
;
^{[2]}
 Naval Research Lab., Washington, DC (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Report Number(s):
 SAND20158754J
Journal ID: ISSN 1070664X; PHPAEN; 615227
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 12; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; magnetic fields; Rayleigh Taylor instabilities; eigenvalues; boundary value problems; kinematics
 OSTI Identifier:
 1239149
 Alternate Identifier(s):
 OSTI ID: 1234031
Velikovich, A. L., and Schmit, P. F.. BellPlesset effects in RayleighTaylor instability of finitethickness spherical and cylindrical shells. United States: N. p.,
Web. doi:10.1063/1.4938272.
Velikovich, A. L., & Schmit, P. F.. BellPlesset effects in RayleighTaylor instability of finitethickness spherical and cylindrical shells. United States. doi:10.1063/1.4938272.
Velikovich, A. L., and Schmit, P. F.. 2015.
"BellPlesset effects in RayleighTaylor instability of finitethickness spherical and cylindrical shells". United States.
doi:10.1063/1.4938272. https://www.osti.gov/servlets/purl/1239149.
@article{osti_1239149,
title = {BellPlesset effects in RayleighTaylor instability of finitethickness spherical and cylindrical shells},
author = {Velikovich, A. L. and Schmit, P. F.},
abstractNote = {BellPlesset (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 RayleighTaylor instability in radiationdriven spherical capsules and magneticallydriven 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 finitethickness shells through acceleration and deceleration phases. The timedependent 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 efoldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thinshell perturbationequations and approximate thinshell 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)].},
doi = {10.1063/1.4938272},
journal = {Physics of Plasmas},
number = 12,
volume = 22,
place = {United States},
year = {2015},
month = {12}
}