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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. and Fukumoto, Y. and Goddard, W. A., III and Abarzhi, S. I. (2018) Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method. Physics of Plasmas, 25 (11). Art. No. 112105. ISSN 1070-664X. http://resolver.caltech.edu/CaltechAUTHORS:20181108-135714511

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.5008648DOIArticle
ORCID:
AuthorORCID
Goddard, W. A., III0000-0003-0097-5716
Additional Information:© 2018 Published by AIP Publishing. Received 9 October 2017; accepted 19 October 2018; published online 8 November 2018. This work was supported by the University of Western Australia (AUS) via the project grant 10101047, the National Science Foundation (USA) via the award 1404449, the Japan Society for Promotion of Science (Japan) via the award S11140, the Caltech SURF program (USA) via the Toni and Bob Perpall SURF Fellowship in 2017, the Department of Energy (USA) via the award DE-SC0017710. The authors contributed to the work as follows: SIA designed research; DVI and SIA performed research; DVI, WAG, and SIA analyzed data; DVI, YF, WAG, and SIA discussed results; and DVI, WAG, and SIA wrote the paper.
Funders:
Funding AgencyGrant Number
University of Western Australia10101047
NSFPHY-1404449
Japan Society for the Promotion of Science (JSPS)S11140
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Department of Energy (DOE)DE-SC0017710
Other Numbering System:
Other Numbering System NameOther Numbering System ID
WAG1259
Record Number:CaltechAUTHORS:20181108-135714511
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181108-135714511
Official Citation: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, Y. Fukumoto, W. A. Goddard III, and S. I. Abarzhi. Physics of Plasmas 2018 25:11
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90762
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Nov 2018 04:14
Last Modified:02 Mar 2019 01:19

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