On the fundamentals of Rayleigh-Taylor dynamics with variable acceleration

Aklant K. Bhowmick, Desmond L. Hill, Snezhana Abarzhi

Research output: Contribution to specialist publicationArticle

Abstract

Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to interfacial shear, find continuous family of regular asymptotic solutions, and discover invariance properties of nonlinear RTI. Our results reveal the interfacial and multi-scale character of RTI with variable acceleration. The former is exhibited in structure of flow fields with intense fluid motion near the interface and effectively no motion in the bulk; the latter follows from the invariance properties of nonlinear dynamics defined by the interplay of two macroscopic length-scales - the wavelength and the amplitude. Our theory resolves the long-standing problem of RTI nonlinear dynamics, achieves excellent agreement with observations, and elaborates diagnostic benchmarks for future experiments and simulations.
Original languageEnglish
Specialist publicationarXiv preprint
Publication statusUnpublished - 2019

Fingerprint

Taylor instability
invariance
group theory
time dependence
supernovae
flow distribution
fusion
shear
fluids
wavelengths

Cite this

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title = "On the fundamentals of Rayleigh-Taylor dynamics with variable acceleration",
abstract = "Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to interfacial shear, find continuous family of regular asymptotic solutions, and discover invariance properties of nonlinear RTI. Our results reveal the interfacial and multi-scale character of RTI with variable acceleration. The former is exhibited in structure of flow fields with intense fluid motion near the interface and effectively no motion in the bulk; the latter follows from the invariance properties of nonlinear dynamics defined by the interplay of two macroscopic length-scales - the wavelength and the amplitude. Our theory resolves the long-standing problem of RTI nonlinear dynamics, achieves excellent agreement with observations, and elaborates diagnostic benchmarks for future experiments and simulations.",
author = "Bhowmick, {Aklant K.} and Hill, {Desmond L.} and Snezhana Abarzhi",
year = "2019",
language = "English",
journal = "arXiv preprint",
publisher = "Cornell University, Ithaca, NY",

}

On the fundamentals of Rayleigh-Taylor dynamics with variable acceleration. / Bhowmick, Aklant K.; Hill, Desmond L.; Abarzhi, Snezhana.

In: arXiv preprint, 2019.

Research output: Contribution to specialist publicationArticle

TY - GEN

T1 - On the fundamentals of Rayleigh-Taylor dynamics with variable acceleration

AU - Bhowmick, Aklant K.

AU - Hill, Desmond L.

AU - Abarzhi, Snezhana

PY - 2019

Y1 - 2019

N2 - Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to interfacial shear, find continuous family of regular asymptotic solutions, and discover invariance properties of nonlinear RTI. Our results reveal the interfacial and multi-scale character of RTI with variable acceleration. The former is exhibited in structure of flow fields with intense fluid motion near the interface and effectively no motion in the bulk; the latter follows from the invariance properties of nonlinear dynamics defined by the interplay of two macroscopic length-scales - the wavelength and the amplitude. Our theory resolves the long-standing problem of RTI nonlinear dynamics, achieves excellent agreement with observations, and elaborates diagnostic benchmarks for future experiments and simulations.

AB - Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to interfacial shear, find continuous family of regular asymptotic solutions, and discover invariance properties of nonlinear RTI. Our results reveal the interfacial and multi-scale character of RTI with variable acceleration. The former is exhibited in structure of flow fields with intense fluid motion near the interface and effectively no motion in the bulk; the latter follows from the invariance properties of nonlinear dynamics defined by the interplay of two macroscopic length-scales - the wavelength and the amplitude. Our theory resolves the long-standing problem of RTI nonlinear dynamics, achieves excellent agreement with observations, and elaborates diagnostic benchmarks for future experiments and simulations.

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