发表机构
The Open University of Israel; The George Washington University; CNRS – Université Paris Cité; Institute of Science, Banaras Hindu University（以色列开放大学; 乔治华盛顿大学; 法国国家科学研究中心-巴黎西岱大学; 贝拿勒斯印度教大学理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对相对论性冷壳层与理想反射壁的斜碰撞问题，利用积分守恒定律在附着区域给出完全解析解，揭示了弱激波与强激波解的存在范围及分离线条件。
AI 中文摘要
相对论性流动在天体物理学中很常见，当流动的不同部分以相对论性相对速度碰撞时，通常会形成激波。这种碰撞往往是斜碰撞，形成两个激波，其激波后的流体被一个接触间断分开，这里将该接触间断视为一个理想的反射“壁”，壁两侧的流动分别建模。后者在实验室坐标系 $S$ 中建模为一个均匀的冷平面壳层，以速度 $v_1=\beta_1c$ 垂直于其真空界面传播，并以入射角 $\alpha_1$ 与壁碰撞。碰撞点 $P$ 沿壁以速度 $v_p=v_{1}/\sin\alpha_1$ 运动，沿壁以 $v_p$ 进行加速导致一个稳态坐标系 $S'$，在该坐标系中该问题被大大简化。然而，存在一个“超光速”区域，其中 $v_p>c\Leftrightarrow\tan\alpha_1<\Gamma_{1}\beta_{1}=(1-\beta_{1}^2)^{-1/2}\beta_1$，且不存在稳态坐标系 $S'$。在牛顿区域，这仅对应于非常小的 $\alpha_1$，但在相对论区域，几乎对应于所有 $\alpha_1$。我们使用积分守恒定律，在点 $P$ 附着于壁的附着区域内，完全解析地解决了该问题。该参数空间区域在高 $\alpha_1$ 端由分离线界定，该分离线与冷初始壳层的声线重合。弱激波解存在于整个该区域，而强激波解仅存在于亚光速附着区域——即在光速线与分离/声线之间，在该线上两种解重合，超过该线后点 $P$ 从壁分离，激波后流体泄漏到真空中。
英文摘要
Relativistic flows are common in astrophysics and often form shocks when different parts of the flow collide at relativistic relative velocities. Such collisions are often oblique, forming two shocks whose shocked fluids are separated by a contact discontinuity, which is treated here as an ideal reflecting ``wall'' where the flow on either side is modeled separately. The latter is modeled in the lab frame $S$ as a uniform cold planar shell propagating into vacuum at velocity $v_1=β_1c$ normal to its vacuum interface, colliding with the wall at an incidence angle $α_1$. The collision point $P$ moves along the wall at a velocity $v_p=v_{1}/\sinα_1$, and a boost along the wall at $v_p$ leads to a steady-state frame $S'$ where this problem is highly simplified. However, a ``super-luminal'' regime exists where $v_p>c\Leftrightarrow\tanα_1<Γ_{1}β_{1}=(1-β_{1}^2)^{-1/2}β_1$ and no steady-state frame $S'$ exists. It corresponds to only very small $α_1$ in the Newtonian regime, but nearly all $α_1$ in the relativistic regime. We solve this problem \textit{\textbf{fully analytically}} using integral conservation laws, in the attachmrnt region where point $P$ is attached to the wall. This region of parameter space is bound at high $α_1$ by the detachment line, which coincides with the sonic line for a cold initial shell. A weak-shock solution exist in all this region, while a strong-shock solution exists only in the sub-luminal attachment region -- between the luminal line and the detachment/sonic line where the two solutions coincide and beyond which point $P$ detaches from the wall and shocked fluid spills into the vacuum.
Comments17 pages, 21 figures, submitted to Physics of Fluids
