Chapter

Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

January 2005

DOI:10.1142/9781860947278_0019

Authors:

Ben-Gurion University of the Negev

Daniela Kartoon

Ben-Gurion University of the Negev

Show all 16 authorsHide

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers (A) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h ∼ α · A · gt2 with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h ∼ tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with tune of the Kelvin-Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.

ResearchGate has not been able to resolve any citations for this publication.

ResearchGate has not been able to resolve any references for this publication.

Article

Scaling Laws of Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Two and Three Dimen...

August 2000 · Comptes Rendus de l Académie des Sciences - Series IV - Physics-Astrophysics

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers ( A ) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as ... [Show full abstract] h∼α·A·gt2 with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h∼tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin–Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.RésuméL'évolution non linéaire, à long terme, des instabilités Rayleigh–Taylor (RT) et Richtmyer–Meskov (RM) à perturbations initiales aléatoires est étudiée au moyen d'un modèle de mécanique statistique basé sur la compétition de bulles ayant tous les nombres d'Atwood ( A ), et à l'aide de simulations numériques complètes à deux et trois dimensions. Les résultats montrent que les fronts de la zone de mélange RT de bulles et d'aiguilles varient comme h∼αA·gt2 avec différentes valeurs de α pour les fronts de bulles et d'aiguilles. Les fronts de la zone de mélange RM varient comme h∼tθ avec différentes valeurs de θ pour les bulles et pour les aiguilles. Une analyse similaire donne une croissance linéaire en fonction du temps pour la zone de mélange Kelvin–Helmholtz. La dépendance des paramètres d'échelle RT et RM en fonction de A et de la dimension est discutée. Les prédictions des simulations à trois dimensions sont en bon accord avec des expériences récentes.

Article

Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling...

June 2001 · Physics of Plasma

The late-time nonlinear evolution of the three-dimensional (3D) Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities for random initial perturbations is investigated. Using full 3D numerical simulations, a statistical mechanics bubble-competition model, and a Layzer-type drag-buoyancy model, it is shown that the RT scaling parameters, αB and αS, are similar in two and three dimensions, ... [Show full abstract] but the RM exponents, θB and θS are lower by a factor of 2 in three dimensions. The similarity parameter hB/〈λ〉 is higher by a factor of 3 in the 3D case compared to the 2D case, in very good agreement with recent Linear Electric Motor (LEM) experiments. A simple drag-buoyancy model, similar to that proposed by Youngs [see J. C. V. Hanson et al., Laser Part. Beams 8, 51 (1990)], but using the coefficients from the A = 1 Layzer model, rather than phenomenological ones, is introduced. © 2001 American Institute of Physics.

Last Updated: 29 May 2025