TY - JOUR
T1 - Perspective
T2 - group theory analysis and special self-similarity classes in Rayleigh–Taylor and Richtmyer–Meshkov interfacial mixing with variable accelerations
AU - Abarzhi, Snezhana I.
N1 - Publisher Copyright:
© Division of Plasma Physics, Association of Asia Pacific Physical Societies 2024.
PY - 2024/12
Y1 - 2024/12
N2 - Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing govern a broad range of processes in nature and technology, at astrophysical and at molecular scales. They are a source of paradigm shifts in science, mathematics, and engineering. In realistic environments, RT/RM dynamics are often caused by variable accelerations. This work employs the group theory to systematically approach RT/RM dynamics with accelerations varying as power law in time and in space, through the direct link of the governing equations to the momentum model. We identify characteristics of RT dynamics and RM dynamics and RT-to-RM transitions, and investigate symmetries, invariant forms, scaling relations, correlations, fluctuation, and spectra of scale-invariant RT mixing and RM mixing. For accelerations varying in time and in space, we discover special self-similarity classes of RT/RM mixing, and explore attributes of their point and interval sub-classes. Depending upon the accelerations, the scale-invariant RT dynamics can be ballistic, quasi-Kolmogorov, steady flex, and quasi-diffusive; it can also belong to the associated super- and sub-intervals; the scale-invariant RM dynamics is sub-diffusive. For any acceleration, RT/RM mixing retains memory of the deterministic (initial and flow) conditions. These characteristics significantly impact the understanding of RT/RM relevant processes in nature, open perspectives unexplored before for better control of RT/RM instabilities in technology, and advance modeling capabilities of RT/RM dynamics in fluids, plasmas, and materials.
AB - Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing govern a broad range of processes in nature and technology, at astrophysical and at molecular scales. They are a source of paradigm shifts in science, mathematics, and engineering. In realistic environments, RT/RM dynamics are often caused by variable accelerations. This work employs the group theory to systematically approach RT/RM dynamics with accelerations varying as power law in time and in space, through the direct link of the governing equations to the momentum model. We identify characteristics of RT dynamics and RM dynamics and RT-to-RM transitions, and investigate symmetries, invariant forms, scaling relations, correlations, fluctuation, and spectra of scale-invariant RT mixing and RM mixing. For accelerations varying in time and in space, we discover special self-similarity classes of RT/RM mixing, and explore attributes of their point and interval sub-classes. Depending upon the accelerations, the scale-invariant RT dynamics can be ballistic, quasi-Kolmogorov, steady flex, and quasi-diffusive; it can also belong to the associated super- and sub-intervals; the scale-invariant RM dynamics is sub-diffusive. For any acceleration, RT/RM mixing retains memory of the deterministic (initial and flow) conditions. These characteristics significantly impact the understanding of RT/RM relevant processes in nature, open perspectives unexplored before for better control of RT/RM instabilities in technology, and advance modeling capabilities of RT/RM dynamics in fluids, plasmas, and materials.
KW - Fluid instabilities
KW - Group theory
KW - Interfacial mixing
KW - Scaling laws
KW - Self-similar dynamics
UR - http://www.scopus.com/inward/record.url?scp=85190458505&partnerID=8YFLogxK
U2 - 10.1007/s41614-023-00142-3
DO - 10.1007/s41614-023-00142-3
M3 - Article
AN - SCOPUS:85190458505
VL - 8
JO - Reviews of Modern Plasma Physics
JF - Reviews of Modern Plasma Physics
IS - 1
M1 - 15
ER -