Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

D. V. Ilyin, Yasuhide Fukumoto, W. A. Goddard, S. I. Abarzhi

Research output: Contribution to journalArticle

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Abstract

We develop a general matrix method to analyze from a far field the dynamics of an accelerated interface between incompressible ideal fluids of different densities with interfacial mass flux and with negligible density variations and stratification. We rigorously solve the linearized boundary value problem for the dynamics conserving mass, momentum, and energy in the bulk and at the interface. We find a new hydrodynamic instability that develops only when the acceleration magnitude exceeds a threshold. This critical threshold value depends on the magnitudes of the steady velocities of the fluids, the ratio of their densities, and the wavelength of the initial perturbation. The flow has potential velocity fields in the fluid bulk and is shear-free at the interface. The interface stability is set by the interplay of inertia and gravity. For weak acceleration, inertial effects dominate, and the flow fields experience stable oscillations. For strong acceleration, gravity effects dominate, and the dynamics is unstable. For strong accelerations, this new hydrodynamic instability grows faster than accelerated Landau-Darrieus and Rayleigh-Taylor instabilities. For given values of the fluids' densities and their steady bulk velocities, and for a given magnitude of acceleration, we find the critical and maximum values of the initial perturbation wavelength at which this new instability can be stabilized and at which its growth is the fastest. The quantitative, qualitative, and formal properties of the accelerated conservative dynamics depart from those of accelerated Landau-Darrieus and Rayleigh-Taylor dynamics. New diagnostic benchmarks are identified for experiments and simulations of unstable interfaces.

Original languageEnglish
Article number112105
JournalPhysics of Plasmas
Volume25
Issue number11
DOIs
Publication statusPublished - Nov 1 2018

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matrix methods
discontinuity
flow distribution
hydrodynamics
fluids
interface stability
stable oscillations
gravitation
ideal fluids
perturbation
potential flow
thresholds
Taylor instability
stratification
boundary value problems
wavelengths
inertia
far fields
velocity distribution
shear

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method. / Ilyin, D. V.; Fukumoto, Yasuhide; Goddard, W. A.; Abarzhi, S. I.

In: Physics of Plasmas, Vol. 25, No. 11, 112105, 01.11.2018.

Research output: Contribution to journalArticle

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