具有Tait-Murnaghan状态方程的可压缩欧拉流体中空腔坍塌的幂律奇异性
Power law singularity for cavity collapse in a compressible Euler fluid with Tait-Murnaghan equation of state
AI总结：
本研究受气泡坍塌高能量聚焦现象启发，采用相似理论方法拓展计算了具有Tait-Murnaghan状态方程的可压缩欧拉流体空腔坍塌幂律指数，得到指数随状态方程参数的变化关系，证实坍塌对流体状态方程敏感。
摘要：
受快速坍塌气泡中发现的高能量聚焦现象的启发——该现象与声致发光等能量密度集中的内爆过程相关，我们对可压缩欧拉流体中的空腔坍塌进行了计算。我们回顾并采用了基于相似理论的方法，该方法此前曾用于计算水中空腔坍塌后期阶段的幂律指数$n$。我们通过考虑空腔周围的不同流体拓展了这一计算，所有流体均通过参数$γ$由Tait-Murnaghan状态方程进行参数化。结果表明，我们得到了宽$γ$范围内$n$随$γ$的变化关系，且确实发现坍塌过程对外部流体的状态方程具有敏感性。
英文摘要：
Motivated by the high energy focusing found in rapidly collapsing bubbles that is relevant to implosion processes that concentrate energy density, such as sonoluminescence, we consider a calculation of an empty cavity collapse in a compressible Euler fluid. We review and then use the method based on similarity theory that was previously used to compute the power law exponent $n$ for the collapse of an empty cavity in water during the late stage of the collapse. We extend this calculation by considering different fluids surrounding the cavity, all of which are parametrized by the Tait-Murnaghan equation of state through parameter $γ$. As a result, we obtain the dependence of $n$ on $γ$ for a wide range of $γ$, and indeed see that the collapse is sensitive to the equation of state of an outside fluid.
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