论文标题
几乎等温的绝热冲击波的结构
The structure of nearly isothermal, adiabatic shockwaves
论文作者
论文摘要
具有时间依赖性半径$ r（t）$的爆炸性产生的冲击波的特征在于一个阶段，在该阶段中，震动的气体具有有效的绝热指数$γ\ simeq 1 $。 Using the result that the post-shock gas is compressed into a shell of width $ΔR/R \simeq δ$, where $δ= γ-1$, we show that a choice of self-similar variable that exploits this compressive behavior in the limit that $γ\rightarrow 1$ naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity $δ$.我们证明，当$γ\ rightarrow 1 $中，前阶（以$δ$为单位）的解决方案可以以简单的，封闭的形式写成，当液体仍然近似为能量持续的状态（即Sedov-Taylor限制），并且密度在震惊之后呈梯度下降。我们还分析了与周围环境相互作用的恒星或银河风周围气泡的解决方案，并为接触不连续性的位置提供表达式，从而将令人震惊的环境气体与震惊的风中分开。我们讨论了我们发现的含义，在几乎等热冲击的动态稳定性的背景下。
An explosively generated shockwave with time-dependent radius $R(t)$ is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index $γ\simeq 1$. Using the result that the post-shock gas is compressed into a shell of width $ΔR/R \simeq δ$, where $δ= γ-1$, we show that a choice of self-similar variable that exploits this compressive behavior in the limit that $γ\rightarrow 1$ naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity $δ$. We demonstrate that the leading-order (in $δ$) solutions, which are increasingly accurate as $γ\rightarrow 1$, can be written in simple, closed forms when the fluid is still approximated to be in the energy-conserving regime (i.e., the Sedov-Taylor limit), and that the density declines exponentially rapidly with distance behind the shock. We also analyze the solutions for the bubble surrounding a stellar or galactic wind that interacts with its surroundings, and derive expressions for the location of the contact discontinuity that separates the shocked ambient gas from the shocked wind. We discuss the implications of our findings in the context of the dynamical stability of nearly isothermal shocks.
