Journal of Nonlinear Mathematical Physics

Volume 24, Issue Supplement 1, December 2017, Pages 3 - 17

Solutions of the buoyancy-drag equation with a time-dependent acceleration

Authors
Serge E. Bouquet
CEA/DAM/DIF, Bruyères-le-Châtel, F–91297 Arpajon Cedex, France
Laboratoire univers et théories (LUTH), Observatoire de Paris, Université de recherche Paris sciences et lettres - PSL Research University, CNRS, Université Paris-Diderot, Sorbonne Paris Cité, 5, place Jules Janssen, F–92190 Meudon, France, Serge.Bouquet@cea.fr
Robert ConteRobert.Conte@cea.fr
CEA/DAM/DIF, Bruyères-le-Châtel, F–91297 Arpajon Cedex, France
Centre de mathématiques et de leurs applications, École normale supérieure de Cachan, CNRS, Université Paris-Saclay, 61, avenue du Président Wilson, F–94235 Cachan, France
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Robert.Conte@cea.fr
Vincent Kelsch
CEA/DAM/DIF, Bruyères-le-Châtel, F–91297 Arpajon Cedex, France
Fabien Louvet
CEA/DAM/DIF, Bruyères-le-Châtel, F–91297 Arpajon Cedex, France
Received 21 April 2017, Accepted 2 August 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2017.1418050How to use a DOI?
Keywords
Buoyancy-drag equation, Lie point symmetries, Abel equation
Abstract

We perform the analytic study of the buoyancy-drag equation with a time-dependent acceleration γ(t) by two methods. We first determine its equivalence class under the point transformations of Roger Liouville, and thus for some values of γ(t) define a time-dependent Hamiltonian from which the buoyancy-drag equation can be derived. We then determine the Lie point symmetries of the buoyancy-drag equation, which only exist for values of γ(t) including the previous ones, plus additional classes of accelerations for which the equation is reducible to an Abel equation. This allows us to exhibit two régimes for the asymptotic (large time t) solution of the buoyancy-drag equation. It is shown that they describe a mixing zone driven by the Rayleigh–Taylor instability and the Richtmyer–Meshkov instability, respectively.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - Supplement 1
Pages
3 - 17
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1418050How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Serge E. Bouquet
AU  - Robert Conte
AU  - Vincent Kelsch
AU  - Fabien Louvet
PY  - 2021
DA  - 2021/01
TI  - Solutions of the buoyancy-drag equation with a time-dependent acceleration
JO  - Journal of Nonlinear Mathematical Physics
SP  - 3
EP  - 17
VL  - 24
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1418050
DO  - https://doi.org/10.1080/14029251.2017.1418050
ID  - Bouquet2021
ER  -