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• W2917178049 abstract "We consider Rayleigh-Taylor and Richtmyer-Meshkov instabilities at the interface between two fluids, one or both of which may be viscous. We derive exact analytic expressions for the amplitude $ensuremath{eta}(t)$ in the linear regime when only one of the fluids is viscous. The more general case is solved numerically using Laplace transforms. We compare the exact solutions of the initial-value problem with the approximate solutions of the eigenvalue problem used in a simple expression for $ensuremath{eta}(t)$ in terms of two growth rates, ${ensuremath{gamma}}_{+}$ and ${ensuremath{gamma}}_{ensuremath{-}}$. We then propose a hybrid model as an improvement on the approximate model. The hybrid model is based on the same expression for $ensuremath{eta}(t)$ in terms of ${ensuremath{gamma}}_{ifmmodepmelsetextpmfi{}}$ but uses exact eigenvalues for ${ensuremath{gamma}}_{+}$, the larger growth rate, and a relationship between ${ensuremath{gamma}}_{ensuremath{-}}$ and ${ensuremath{gamma}}_{+}$. We also discuss two concepts: isogrowth wave number pairs and asymptotic decay. The first relies on viscosity in one or both fluids to identify perturbations of two different wavelengths having the same ${ensuremath{gamma}}_{+}$. The second concept, which is more general, can be found in viscous as well as inviscid fluids and requires only a specific initial growth rate ${stackrel{ifmmode dot{}else .{}fi{}}{ensuremath{eta}}}_{0}^{mathrm{critical}}$ to force $ensuremath{eta}(t)ensuremath{rightarrow}0$ as $tensuremath{rightarrow}ensuremath{infty}$. We present several examples illustrating these two concepts and comparing exact, approximate, and hybrid treatments." @default.
• W2917178049 created "2019-03-02" @default.
• W2917178049 creator A5049140708 @default.
• W2917178049 date "2019-02-25" @default.
• W2917178049 modified "2023-09-23" @default.
• W2917178049 title "Exact, approximate, and hybrid treatments of viscous Rayleigh-Taylor and Richtmyer-Meshkov instabilities" @default.
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• W2917178049 doi "https://doi.org/10.1103/physreve.99.023112" @default.
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• W2917178049 hasPublicationYear "2019" @default.
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