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- W2055108601 abstract "Effects of temporal density variation and spherical convergence on the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability are studied using an analytical model based on Layzer's theory [Astrophys. J. 122, 1 (1955)]. When the temporal density variation is included, the bubble amplitude in planar geometry is shown to asymptote to ${ensuremath{int}}^{t}{U}_{L}({t}^{ensuremath{'}})ensuremath{rho}({t}^{ensuremath{'}})d{t}^{ensuremath{'}}∕ensuremath{rho}(t)$, where ${U}_{L}=sqrt{g∕({C}_{g}k)}$ is the Layzer bubble velocity, $ensuremath{rho}$ is the fluid density, and ${C}_{g}=3$ and ${C}_{g}=1$ for the two- and three-dimensional geometries, respectively. The asymptotic bubble amplitude in a converging spherical shell is predicted to evolve as $ensuremath{eta}ensuremath{sim}overline{ensuremath{eta}}{m}^{ensuremath{-}ensuremath{mid}{stackrel{ifmmode dot{}else .{}fi{}}{r}}_{0}ensuremath{mid}∕ensuremath{ell}{U}_{L}^{mathrm{sp}}ensuremath{-}overline{ensuremath{eta}}∕{r}_{0}}$, where ${r}_{0}$ is the outer shell radius, $overline{ensuremath{eta}}(t)={ensuremath{int}}^{t}{U}_{L}^{mathrm{sp}}({t}^{ensuremath{'}})ensuremath{rho}({t}^{ensuremath{'}}){r}_{0}^{2}({t}^{ensuremath{'}})d{t}^{ensuremath{'}}∕ensuremath{rho}(t){r}_{0}^{2}(t)$, ${U}_{L}^{mathrm{sp}}=sqrt{ensuremath{-}{stackrel{ifmmode ddot{}else "{}fi{}}{r}}_{0}(t){r}_{0}(t)∕ensuremath{ell}}$, $m(t)=ensuremath{rho}(t){r}_{0}^{3}(t)$, and $ensuremath{ell}$ is the mode number." @default.
- W2055108601 created "2016-06-24" @default.
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- W2055108601 date "2005-04-26" @default.
- W2055108601 modified "2023-10-18" @default.
- W2055108601 title "Effects of temporal density variation and convergent geometry on nonlinear bubble evolution in classical Rayleigh-Taylor instability" @default.
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- W2055108601 doi "https://doi.org/10.1103/physreve.71.046306" @default.
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