2001
DOI: 10.1017/s0022112001005377
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Transition stages of Rayleigh–Taylor instability between miscible fluids

Abstract: Direct numerical simulations (DNS) are presented of three-dimensional, RayleighTaylor 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-… Show more

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Cited by 220 publications
(168 citation statements)
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“…On the side of the numerical simulations, modelling RT mixing is a severe test, as the numerical solutions appear sensitive to the initial and boundary conditions as well as to the influence of unresolved small-scale structures on the large-scale dynamics and to the anomalous character of energy transport (Gardner et al 1988;Youngs 1991;He et al 1999;Cook & Dimotakis 2001;Young et al 2001;Kadau et al 2007). Addressing these difficulties brings up the issue of predictive capability of the numerical models, their verification and validation as well as quantification of uncertainty of the solutions obtained (Calder et al 2002;George et al 2002).…”
Section: Rayleigh-taylor Phenomenamentioning
confidence: 99%
“…On the side of the numerical simulations, modelling RT mixing is a severe test, as the numerical solutions appear sensitive to the initial and boundary conditions as well as to the influence of unresolved small-scale structures on the large-scale dynamics and to the anomalous character of energy transport (Gardner et al 1988;Youngs 1991;He et al 1999;Cook & Dimotakis 2001;Young et al 2001;Kadau et al 2007). Addressing these difficulties brings up the issue of predictive capability of the numerical models, their verification and validation as well as quantification of uncertainty of the solutions obtained (Calder et al 2002;George et al 2002).…”
Section: Rayleigh-taylor Phenomenamentioning
confidence: 99%
“…Inside the mixing layer, the θ value is equal to 1 when both the fluids are completely molecularly mixed, and θ becomes zero when two fluids are immiscible. In equation (15), ρ is the instantaneous density at a location, whereas ρ is the time-averaged density for a total measurement (16), is also used by many researchers ( [47,48]) to quantify molecular mixing in a fast-kinetic chemical reaction where the product formed is limited by the amount of lean reactant. The definition of Ξ , used by Cook and Dimotakis [47] and Youngs [48], is an integrated parameter across the mixing layer.…”
Section: Molecular Mixing Parameter (θ )mentioning
confidence: 99%
“…From linear stability analysis, the most unstable wavelength decreases with increasing g (8), and thus a value of g Ϸ 1 ϫ 10 10 g Earth is required. Whether such a large g value distorts the instability process depends on whether g is a scalable variable up to that magnitude, which can be validated by comparison with experimental and continuum descriptions of the hydrodynamical problem as described by the Navier-Stokes (NS) equations, which assume scalability (4,6,(8)(9)(10)(11)(12)(13)(14). Furthermore, supernovae explosions with g Ͼ Ͼ g Earth suggest scalability, and although most simulations were performed with that large value of g, an order of magnitude smaller value did not change the results within statistical fluctuations.…”
Section: Rayleigh-taylor (Rt) Instabilitymentioning
confidence: 99%