Second-type self-similar solutions to the ultrarelativistic strong explosion problem
Second-type self-similar solutions to the ultrarelativistic strong explosion problem
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DOI：
10.1063/1.1285921
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发表时间：
2000-10
影响因子：
4.6
通讯作者：
PaulJ. Best;R. Sari
中科院分区：
文献类型：
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作者：
PaulJ. Best;R. Sari
著名的布兰福德-麦基解描述了被强激波包围的球形爆炸波中的超相对论性流动。当激波传播进入的外部介质的密度随距离r的变化而变化时，如r−k （k 5−3/4≈4.13）所示，该公式是有效的。在这些解中Γ随Γ2∝t−m (m=(3−23)k−4（5−33）而变化，因此激波加速，激波附近所含流动能量的比例随时间减少。结果表明，新解与流动方程的数值模拟结果非常吻合。证明了k<5−3/4≈4.13时不存在第二类自相似解。
The well-known Blandford–McKee solution describes the ultrarelativistic flow in a spherical blast wave enclosed by a strong shock. It is valid when the density of the external medium into which the shock propagates varies with the distance r from the origin as r−k, for k 5−3/4≈4.13, are presented. In these solutions Γ varies as Γ2∝t−m with m=(3−23)k−4(5−33) so that the shock accelerates and the fraction of the flow energy contained in the vicinity of the shock decreases with time. The new solutions are shown to be in excellent agreement with numerical simulations of the flow equations. It is proved that no second-type self-similar solutions exist for k<5−3/4≈4.13.