On the fundamentals of Richtmyer-Meshkov dynamics with variable acceleration

Research output: Contribution to specialist publicationArticle

Abstract

Richtmyer-Meshkov instability (RMI) plays important role in nature and technology, from supernovae and fusion to scramjets and nano-fabrication. Canonical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. This work focuses on RMI induced by acceleration with a power-law time-dependence, and applies group theory to solve the classical problem. For early-time dynamics, we find the dependence of RMI growth-rate on the initial conditions and show it is free from 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 the solutions stability. For each of the solutions, the interface dynamics is directly linked to the interfacial shear, and 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 excellent agreement with observations. We elaborate new theory benchmarks for experiments and simulations, and put forward a hypothesis on the role of viscous effects in interfacial nonlinear RMI.
Original languageEnglish
Specialist publicationarXiv preprint
Publication statusPublished - 2019

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shear
supersonic combustion ramjet engines
nanofabrication
group theory
time dependence
supernovae
invariance
velocity distribution
fusion
shock
curvature
fluids
wavelengths
simulation

Cite this

@misc{a85840ad759446cfba093b96b75fd546,
title = "On the fundamentals of Richtmyer-Meshkov dynamics with variable acceleration",
abstract = "Richtmyer-Meshkov instability (RMI) plays important role in nature and technology, from supernovae and fusion to scramjets and nano-fabrication. Canonical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. This work focuses on RMI induced by acceleration with a power-law time-dependence, and applies group theory to solve the classical problem. For early-time dynamics, we find the dependence of RMI growth-rate on the initial conditions and show it is free from 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 the solutions stability. For each of the solutions, the interface dynamics is directly linked to the interfacial shear, and 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 excellent agreement with observations. We elaborate new theory benchmarks for experiments and simulations, and put forward a hypothesis on the role of viscous effects in interfacial nonlinear RMI.",
author = "Bhowmick, {A. K.} and Des Hill and Miccal Matthews and Snezhana Abarzhi",
year = "2019",
language = "English",
journal = "arXiv preprint",
publisher = "Cornell University, Ithaca, NY",

}

On the fundamentals of Richtmyer-Meshkov dynamics with variable acceleration. / Bhowmick, A. K.; Hill, Des; Matthews, Miccal; Abarzhi, Snezhana.

In: arXiv preprint, 2019.

Research output: Contribution to specialist publicationArticle

TY - GEN

T1 - On the fundamentals of Richtmyer-Meshkov dynamics with variable acceleration

AU - Bhowmick, A. K.

AU - Hill, Des

AU - Matthews, Miccal

AU - Abarzhi, Snezhana

PY - 2019

Y1 - 2019

N2 - Richtmyer-Meshkov instability (RMI) plays important role in nature and technology, from supernovae and fusion to scramjets and nano-fabrication. Canonical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. This work focuses on RMI induced by acceleration with a power-law time-dependence, and applies group theory to solve the classical problem. For early-time dynamics, we find the dependence of RMI growth-rate on the initial conditions and show it is free from 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 the solutions stability. For each of the solutions, the interface dynamics is directly linked to the interfacial shear, and 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 excellent agreement with observations. We elaborate new theory benchmarks for experiments and simulations, and put forward a hypothesis on the role of viscous effects in interfacial nonlinear RMI.

AB - Richtmyer-Meshkov instability (RMI) plays important role in nature and technology, from supernovae and fusion to scramjets and nano-fabrication. Canonical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. This work focuses on RMI induced by acceleration with a power-law time-dependence, and applies group theory to solve the classical problem. For early-time dynamics, we find the dependence of RMI growth-rate on the initial conditions and show it is free from 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 the solutions stability. For each of the solutions, the interface dynamics is directly linked to the interfacial shear, and 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 excellent agreement with observations. We elaborate new theory benchmarks for experiments and simulations, and put forward a hypothesis on the role of viscous effects in interfacial nonlinear RMI.

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JO - arXiv preprint

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