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arXiv · 1210.0487

The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension

Ovidiu Costin·Saleh Tanveer·Michael I. Weinstein
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Abstract

General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\sim e^{-Γt}, Γ>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $Γ\approx \frac{A}ε \frac{We}{ε^{2}} \exp(-B \frac{We}{ε^2})$, where $0<ε\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants. In this paper, we prove this conjecture and calculate $A$ and $B$ to leading order in $ε$.

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Ovidiu Costin, Saleh Tanveer, Michael I. Weinstein. 2012-10-01. The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension. https://arxiv.org/abs/1210.0487

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