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Transition stages of Rayleigh–Taylor instability between miscible fluids

Cook, Andrew W. and Dimotakis, Paul E. (2001) Transition stages of Rayleigh–Taylor instability between miscible fluids. Journal of Fluid Mechanics, 443 . pp. 69-99. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:COOjfm01

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Abstract

Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." Received June 2 2000, Revised March 28 2001, Published Online 25 September 2001. This work was performed under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory, under contract No. W-7405-Eng-48, the DOE/Caltech ASCI/ASAP subcontract B341492, and the Air Force Office of Scientific Research Grant Nos. F49620-94-1-0353 and F49620-98-1-0052. The authors would like to acknowledge advice from R. D. Henderson on the pressure boundary conditions, discussions and assistance with the text by P. L. Miller and D. Pullin, discussions with D. I. Meiron, and assistance with exploratory computer visualization by S. B. Deusch, S. V. Lombeyda, and J. M. Patton based on the results of the earlier runs.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48
Department of Energy (DOE)B341492
Air Force Office of Scientific Research (AFOSR)F49620-94-1-0353
Air Force Office of Scientific Research (AFOSR)F49620-98-1-0052
Record Number:CaltechAUTHORS:COOjfm01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:COOjfm01
Alternative URL:http://dx.doi.org/10.1017/S0022112001005377
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1899
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:23 Feb 2006
Last Modified:19 Nov 2018 23:00

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