The Mach Reflection of Shock Waves at Nearly Glancing Incidence
The Mach Reflection of Shock Waves at Nearly Glancing Incidence
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DOI：
10.1103/revmodphys.23.271
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发表时间：
1951-07
影响因子：
44.1
通讯作者：
C. H. Fletcher;W. Bleakney
中科院分区：
文献类型：
--
作者：
C. H. Fletcher;W. Bleakney
对空气中平面激波与平面刚性壁相互作用的实验研究表明，这种反射现象至少有两种形式，如图1所示：（a）规则反射，即原激波或入射激波之后有一个反射激波，它在壁面上与入射激波汇合;（B）马赫反射，即反射激波与入射激波在一个三重点（或线）上汇合，该三重点（或线）离壁面有一定距离，并由第三个激波（通常是弯曲的）与壁面汇合，该三重点（或线）称为马赫激波。对于任意给定（有限）强度的激波，如果激波入射足够接近掠射，则总是发生马赫反射，如果激波入射足够接近迎面，则总是发生规则反射。由于马赫反射问题的非线性性质，以及由分析确定的反射激波和马赫激波的位置和强度也规定了Qow的边界条件，因此很难用完整的数学方法来解决这个问题。然而，可以作出各种不同的解释，它们不考虑问题的非线性特征，而只考虑马赫反射的三重点附近的条件，或规则反射的入射激波和反射激波的交点附近的条件。这些处理基本上是局部性的，在参考文献[1]中作了详细介绍。这个问题基本上是二维问题，通常考虑激波与垂直于壁面和入射激波的平面相交的构形。在考虑这些局部问题时，通常方便的做法是在所讨论的点上选择原点，并将其归为静止。当这样做时，
An experimental investigation of the interaction of a plane shock wave in air with a plane rigid wall reveals that this reQection phenomenon takes at least the two formswhich are illustrated in Fig. 1:(a) regular reflection in which the original or incident shock is followed by a reQected shock which joins the incident shock wave at the wall and (b) Machreflection in which the reflected shock meets the incident shock at a triple point (or line) which is some distance from the wall and is joinedto it by a third shock wave (usually curved) called the Mach shock. For the case of a shock wave of any specified(finite) strength, Mach reflection will always occur if the incidence is suKciently near glancing and regular reflection will occur if the incidence of the shock wave on the wall is sufIiciently near head-on. In an earlier paper'this problem was discussed prin-cipally from a theoreticalviewpoint. A complete mathematical solution to the problem of Mach reflection is very difFicult because of the nonlinear nature of the problem and the fact that the location and strengths of the reQected and Mach shocks which are to bede-termined by the analysis also specify the boundary conditions for the Qow. Nevertheless, various assump-tions can be made which do not aGect the nonlinear character of the problem but treat the conditions in the vicinity of the triple point for Mach reflection or, for regular reflection, the conditions near the intersection of the incident and reflected shocks. These treatments are fundamentally local in character and are made in detail in reference 1.The problem is essentially a two-dimensional one, and it is usual to consider the configuration of the intersections of the shock waves with a plane which is perpendicular to the wall and to the incident shock. In considering these local problems it is usually convenient to choose the origin at the point in question and reduce it to rest. When this is done, the conditions for