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Related Experiment Video

Updated: Jun 11, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Nonideal Rayleigh-Taylor mixing.

Hyunkyung Lim¹, Justin Iwerks, James Glimm

¹Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.

Proceedings of the National Academy of Sciences of the United States of America

|July 10, 2010

Summary

Rayleigh-Taylor mixing is indeterminate due to nonideal factors like initial conditions and regularizations. Numerical simulations show the mixing rate depends on these factors, not just ideal fluid dynamics.

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Area of Science:

Fluid Dynamics
Hydrodynamic Instabilities
Computational Physics

Background:

Rayleigh-Taylor (RT) mixing is a fundamental hydrodynamic instability.
Deviations from ideal Euler equations arise from physical/numerical regularizations and nonideal initial conditions.
Kolmogorov's turbulence theory predicts scale-invariant stirring for ideal Euler equations.

Purpose of the Study:

To investigate the impact of nonideal factors on Rayleigh-Taylor mixing rates.
To provide numerical evidence for the indeterminacy of RT mixing in the large Reynolds number limit.
To explore the dependence of mixing on regularization parameters and initial conditions.

Main Methods:

Utilized a large eddy simulation (LES) algorithm for numerical modeling.
Performed mesh convergence studies to ensure solution accuracy.
Investigated the influence of Schmidt and Prandtl numbers (laminar and turbulent) on mixing.
Analyzed the effect of both short and long wavelength initial perturbations.

Main Results:

Demonstrated that RT mixing rate depends on nonideal regularizations, leading to nonunique solutions in the Euler equation limit.
Showed that mesh convergence requires explicit use of Schmidt and Prandtl numbers, including turbulent counterparts.
Illustrated the dependence of mixing rate on Schmidt and Prandtl numbers and other physical parameters.
Confirmed that both short and long wavelength initial conditions significantly influence the mixing rate.

Conclusions:

The study confirms the indeterminacy of Rayleigh-Taylor mixing when modeled by Euler equations, influenced by nonideal regularizations.
A single universal explanation for RT mixing is absent; contributions from initial conditions and regularizations vary.
Accurate modeling requires accounting for physical and numerical regularizations and specific initial conditions.