ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In the collapse of a spherical cavity surrounded by a perfect gas initially at rest, the velocity R(overdot) of the free gas boundary has an initial valve of −2c0/(γ−1) (c0 is the speed of sound in the undisturbed gas and γ is the adiabatic exponent). Hereafter R(overdot) remains practically constant until R becomes a certain fraction ξ(γ) of the initial radius R0. Finally, for R〈ξR0, R(overdot) approaches the asymptotic behavior R(overdot)∼R−τ(γ) predicted by self-similar solutions. The function ξ(γ), which has been obtained numerically, decreases as γ decreases and vanishes for a certain value of γ near 1.5. This fact, together with the analogous behavior of τ(γ), suggests that there exists a certain value γcr≈1.5 of the adiabatic exponent such that, for 1〈γ〈γcr the velocity R(overdot) of the free boundary is strictly a constant during the entire collapse. This behavior seems to be closely related to the results obtained by Lazarus [Phys. Fluids 25, 1146 (1982)] who demonstrates that a degenerate stable, asymptotic solution, with R(overdot)=const, exists for γ〈3/2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.865917
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