AI 中文总结
本文推导了三维激波与弱间断相互作用的局部欧拉连接律，分离散射与几何效应，确定曲率沉积及下游响应，并给出精确数值例证与守恒关系。
AI 中文摘要
弱声学、熵或涡量片可以穿过有限强度的三维激波而不产生折痕，但可以沿相交曲线沉积曲率间断。我们推导了一个局部欧拉连接律，将主动法向平面散射问题与其三维几何实现分开。散射选择一个标量曲率振幅，而激波的取向和预先存在的形状决定完整的曲率张量和下游流动响应。一对受控的鞍点-激波相互作用具有相同的入射和出射模态振幅，但产生的激波后压力梯度矢量相差31.6度，涡量矢量相差25.6度。对于完全气体，声学入射还具有曲率中性分支：出射声学、熵和剪切波保持有限，而曲率通道抵消。对流熵和面内涡量片以相反符号沉积曲率，其系数满足由总焓守恒和声学正交性施加的精确关系；线切向涡量是曲率透明的。一个膨胀的球形激波提供了一个非定常例子，具有非零激波速度和非零相交线跟踪速度，将平滑的爆炸波加速度与沉积的加速度跳跃分开。在脐点附近，同一连接律选择或旋转主曲率框架。所得定律提供了连接光滑弯曲激波重建所需的界面数据，这些重建跨越一个连续可微、分段二次可微的前沿。
英文摘要
A weak acoustic, entropy or vortical sheet can cross a finite-strength three-dimensional shock without producing a kink, yet it can deposit a discontinuity of curvature along the intersection curve. We derive a local Euler junction law that separates the active normal-plane scattering problem from its three-dimensional geometric realization. The scattering selects one scalar curvature amplitude, while the orientation and pre-existing shape of the shock determine the full curvature tensor and the downstream flow response. A controlled pair of saddle-shock interactions has identical incident and outgoing modal amplitudes but produces post-shock pressure-gradient vectors separated by 31.6 degrees and vorticity vectors separated by 25.6 degrees. For a perfect gas, acoustic incidence also possesses curvature-neutral branches: outgoing acoustic, entropy and shear waves remain finite while the curvature channel cancels. Convected entropy and in-plane vortical sheets deposit curvature with opposite signs, and their coefficients obey an exact relation imposed by total-enthalpy conservation and acoustic orthogonality; line-tangent vorticity is curvature-transparent. An expanding spherical shock provides an unsteady example with non-zero shock speed and non-zero intersection-line tracking speed, separating the smooth blast-wave acceleration from the deposited acceleration jump. Near an umbilic, the same junction selects or rotates the principal-curvature frame. The resulting law supplies the interface data needed to connect smooth curved-shock reconstructions across a continuously differentiable, piecewise twice-differentiable front.
Comments19 pages, 4 figures
