On the Rayleigh-Taylor unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration

Abstract

Richtmyer-Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to solve the long-standing problem. For early-time dynamics, we find the dependence of the growth-rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time dynamics, we find a continuous family of regular asymptotic solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and we study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear, the non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that nonlinear coherent dynamics in RMI is characterized by two macroscopic length-scales -the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined, these being respectively, the Atwood, Taylor, convergence, minimum-shear, and critical bubbles, among others. We also elaborate new theory benchmarks for future experiments and simulations.

On Rayleigh-Taylor and Richtmyer-Meshkov Dynamics With Inverse-Quadratic Power-Law Acceleration

“…In applications, this aspect is critical for blast-wave-driven RTI/RMI in core-collapse supernovae, for RT/RM unstable plasma irregularities in the Earth's ionosphere, for RTI/RMI induced by unsteady shocks in inertial confinement fusion, and for RT/RM instabilities in the fossil fuel industry [8][9][10][11][12][13][14][15]. As regards to fundamentals, since classical RTI is driven by the acceleration and classical RMI is driven by the initial growth-rate dependent on the initial conditions, the link between RT and RM dynamics can be self-consistently revealed for variable accelerations, particularly, for accelerations whose magnitudes vary as power-laws in time [8,[46][47][48][49]. Power-law functions are important to consider because they can yield special invariant and scaling properties of RT/RM dynamics, and can also be used to adjust the acceleration's time-dependence in applications [8,[46][47][48][49].…”

“…As regards to fundamentals, since classical RTI is driven by the acceleration and classical RMI is driven by the initial growth-rate dependent on the initial conditions, the link between RT and RM dynamics can be self-consistently revealed for variable accelerations, particularly, for accelerations whose magnitudes vary as power-laws in time [8,[46][47][48][49]. Power-law functions are important to consider because they can yield special invariant and scaling properties of RT/RM dynamics, and can also be used to adjust the acceleration's time-dependence in applications [8,[46][47][48][49].…”

“…By applying group theory approach, recent research on RTI/ RMI with variable acceleration, which has magnitude g Gt a with G, a being respectively the acceleration's strength and exponent, found the dependence of RTI/RMI dynamics on the exponent a of the acceleration's power-law [8,[46][47][48][49] The linear and nonlinear interfacial dynamics is of RT type and is driven by the acceleration with magnitude g Gt a for the acceleration exponents greater than negative two, a >−2 [8,[46][47][48][49]. It is of RM type and is driven by the initial growth rate with magnitude v 0 for the acceleration exponents smaller than negative 2, a <−2.…”

“…It is of RM type and is driven by the initial growth rate with magnitude v 0 for the acceleration exponents smaller than negative 2, a <−2. The properties of the scale-dependent RT and RM dynamics differ substabtially from one another in both the linear or nonlinear regimes [8,[46][47][48][49]. Detailed investigation is thus required of RT/ RM dynamics and RT-to-RM transition at the acceleration exponent equal to negative two, a −2 [8].…”

Effect of dimensionality and symmetry on scale-dependent dynamics of Rayleigh–Taylor instability

“…Recent approaches have striven to marry the results of the drag-buoyancy model to a potential-flow model, as well as extend the efficacy of the various approaches to include more scenarios than a planar configuration undergoing a constant acceleration. Significant progress has been achieved in the study of Rayleigh-Taylor dynamics, with the group theory based approach finding solutions for the scale-dependent and self-similar dynamics in constant, impulsive and time-varying accelerations in a broad range of geometries and configurations (Abarzhi 1998, 2010, Anisimov et al 2013, Hill and Abarzhi 2019, Abarzhi and Williams 2020. Particularly, the group theory approach has found the multi-scale character of nonlinear RTI and the order in RT mixing (Abarzhi 1998, 2008a, 2010, and has explained a broad set of experiments in plasmas and fluids observing that RT mixing may keep order at high Reynolds numbers up to 3.2 million (Anisimov et al 2013, Swisher et al 2015, Meshkov and.…”