On the miscible Rayleigh–Taylor instability: two and three dimensions

By Yuan-Nan Young, H. Tufo, Anshu Dubey, R. Rosner. Journal of Fluid Mechanics, 2001

181 citations recorded by the source corpus.

We investigate the miscible Rayleigh–Taylor (RT) instability in both two and three dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: we identify three distinct evolutionary phases in this development, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed differences between two- and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (i) work equally well for both laminar and turbulent flows, and (ii) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and their interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (for single plumes) to a simple analytical model for plume evolution.

Subfields: Computational Mechanics, Nuclear and High Energy Physics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/92c3fee9c1cdbf6ef57f37b6d8964b611ed573fa

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Citations in the corpus

Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers (2004, methodology): “03 from numerical simulations (Young et al. 2001; Youngs 1984), while experimental values are usually higher.”
A high‐resolution hybrid scheme for hyperbolic conservation laws (2015, background): “Rayleigh–Taylor instability This problem has been simulated extensively by many authors [20, 21] to assess the inherent numerical viscosities of the numerical schemes.”
Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations (2004, background): “Good historical summaries of Rayleigh–Taylor simulations are given in recent articles by Dalziel et al. (1999) and Young et al. (2001).”
Resolution of high order WENO schemes for complicated flow structures (2003, background): “bubbles of light fluid rising into the ambient heavy fluid and spikes of heavy fluid falling into the light fluid, see for example [5] and [13].”
Incompressible Rayleigh–Taylor Turbulence (2017, background): “The K41 scenario was also confirmed in high-resolution numerical simulations (e.g., Young et al. 2001, Dimonte et al. 2004, Cabot & Cook 2006).”
DIRECT NUMERICAL SIMULATION OF RADIATION PRESSURE-DRIVEN TURBULENCE AND WINDS IN STAR CLUSTERS AND GALACTIC DISKS (2012, background): “Even for simple fluid RayleighTaylor instability the relationship between two- and three-dimensional results is still not fully understood, though numerical results indicate the non-linear growth rate is a factor of ∼ 2 faster in the 3D case (e.g. Young et al. 2001, and references therein).”
On Validating an Astrophysical Simulation Code (2002, result): “We confirm previous findings (Kane et al. 2000; Young et al. 2001) that instability growth rates in three-dimensional simulations are larger than those found in the equivalent two-dimensional simulations, which indicates limits on results from two-dimensional models of astrophysical phenomena.”