58 



HYDRODYNAMICAL RELATIONS 



condition for this problem being that the particle velocity at the plane 

 of symmetry through the line of intersection has no component normal 

 to the plane. The necessary result is therefore the solution for the 

 rigid boundary plus the reflection of this solution in the boundary. The 

 question of rigidity disappears, and the validity of the solution involves 

 only the assumption that shearing effects can be neglected. Inter- 

 secting shock waves are at least an approximation to the circumstances 

 involved in pressure waves from multiple charges or different parts of a 

 single nonspherical charge, and the discussion following is thus signifi- 

 cant in such situations. 



We saw, at the beginning of this section, that an oblique shock wave 

 striking a rigid surface leaves the fluid behind it with a component of 



,a ) FIXED FRAME OF REFERENCE 



Fig. 2.10 Oblique reflection of a shock front at a rigid boundary 



(b) FRAME MOVING, POINT OF 

 CONTACT STATIONARY 



flow toward the surface and that the necessity of reducing this com- 

 ponent to zero requires that a reflected wave be developed. The 

 simple scheme of mirror reflection was found to hold for a very weak 

 disturbance, but must now be re-examined. In the situation of Fig. 

 2.10(a), the flow velocity u behind OS can no longer be considered 

 infinitesimal. The physical situation actually realized must be one 

 which reduces the component of u normal to the boimdary to zero. 

 Whether or not a single reflected shock OR can do this is the first con- 

 sideration. If Fig. 2.10 is to apply at all times it must be true that the 

 velocity of OR parallel to itself is just equal to that of the incident wave 

 OS, otherwise OR will get ahead of itself, so to speak, and leave a situ- 

 ation at and near incompatible with the boundary condition. Pre- 

 cisely this must happen, however, as the angle of incidence a apj^roachcs 

 90°. For in this case, the particle velocity u will be nearly noi-mal to 

 the front OR and the fluid ahead of OR has an increasingly large com- 

 ponent of velocity normal to OR for any assumed angle a. The pres- 



