Solutions of the buoyancy-drag equation with a time-dependent acceleration
- 10.1080/14029251.2017.1418050How to use a DOI?
- Buoyancy-drag equation; Lie point symmetries; Abel equation
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.
- © 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 - 2021/01/06 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 - 10.1080/14029251.2017.1418050 ID - Bouquet2021 ER -