TY - JOUR
T1 - Buoyancy and drag in Rayleigh–Taylor and Richtmyer–Meshkov linear, nonlinear and mixing dynamics
AU - Abarzhi, Snezhana I.
AU - Hill, Desmond L.
AU - Williams, Kurt C.
AU - Wright, Cameron E.
PY - 2022/9
Y1 - 2022/9
N2 - Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing are omnipresent in nature and technology and are long-standing challenges in mathematics. This work reports the first rigorous derivation of the buoyancy and drag values from the conservation laws and the boundary value and initial value problems governing RT/RM dynamics with variable acceleration having power-law time dependence. Within group theory approach, we directly link the governing equations, through the dynamical system based on space groups, to the momentum model based on scaling transformations. We precisely derive the model parameters — the buoyancy and the drag, exactly integrate the model equations, and find asymptotic behaviors of the solutions for RT/RM bubbles and spikes in the linear, nonlinear and mixing regimes. The analysis provides new extensive benchmarks for future research.
AB - Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing are omnipresent in nature and technology and are long-standing challenges in mathematics. This work reports the first rigorous derivation of the buoyancy and drag values from the conservation laws and the boundary value and initial value problems governing RT/RM dynamics with variable acceleration having power-law time dependence. Within group theory approach, we directly link the governing equations, through the dynamical system based on space groups, to the momentum model based on scaling transformations. We precisely derive the model parameters — the buoyancy and the drag, exactly integrate the model equations, and find asymptotic behaviors of the solutions for RT/RM bubbles and spikes in the linear, nonlinear and mixing regimes. The analysis provides new extensive benchmarks for future research.
KW - Group theory
KW - Interfacial mixing
KW - Rayleigh–Taylor instability
KW - Richtmyer–Meshkov instability
UR - http://www.scopus.com/inward/record.url?scp=85127148934&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2022.108036
DO - 10.1016/j.aml.2022.108036
M3 - Article
AN - SCOPUS:85127148934
SN - 0893-9659
VL - 131
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 108036
ER -