TY - JOUR
T1 - An analysis of the buoyancy and drag parameters in Rayleigh-Taylor dynamics
AU - Hill, Des
AU - Abarzhi, Snezhana
N1 - Publisher Copyright:
© 2023 EDP Sciences. All rights reserved.
PY - 2023
Y1 - 2023
N2 - Rayleigh-Taylor instability (RTI) is of critical important in a broad range of natural and industrial processes and is an intellectual challenge for theoretical studies. In this work, we analyze the scale-dependent linear and nonlinear Rayleigh{Taylor (RT) dynamics within the group theory approach. We link the governing equations, through an associated dynamical system based on space groups, to a momentum model based on scaling transformations. In doing so, we precisely derive expressions for the buoyancy and drag parameters of the momentum model, exactly integrate the model equations and determine solutions for bubbles and for spikes in both early-time and late-time regimes. In particular, we focus on the general situation in which the instability is driven by an acceleration having power-law time dependence. Our analysis provides extensive benchmarks for future research.
AB - Rayleigh-Taylor instability (RTI) is of critical important in a broad range of natural and industrial processes and is an intellectual challenge for theoretical studies. In this work, we analyze the scale-dependent linear and nonlinear Rayleigh{Taylor (RT) dynamics within the group theory approach. We link the governing equations, through an associated dynamical system based on space groups, to a momentum model based on scaling transformations. In doing so, we precisely derive expressions for the buoyancy and drag parameters of the momentum model, exactly integrate the model equations and determine solutions for bubbles and for spikes in both early-time and late-time regimes. In particular, we focus on the general situation in which the instability is driven by an acceleration having power-law time dependence. Our analysis provides extensive benchmarks for future research.
KW - Coherent structures
KW - Interfacial dynamics
KW - Rayleigh-Taylor instability
KW - Variable acceleration
UR - http://www.scopus.com/inward/record.url?scp=85176329568&partnerID=8YFLogxK
U2 - 10.1051/mmnp/2023027
DO - 10.1051/mmnp/2023027
M3 - Article
AN - SCOPUS:85176329568
SN - 0973-5348
VL - 18
JO - Mathematical Modelling of Natural Phenomena
JF - Mathematical Modelling of Natural Phenomena
M1 - 29
ER -