HYDRODYNAMICAL RELATIONS 49 



be set up only if we postulate a secondary shock front originating at 

 of such strength and direction that its passage through the fluid be- 

 hind OS introduces a normal velocity equal and opposite to that pro- 

 duced by the incident wave all along the line OB'. A conceivable front 

 of this kind is indicated by the dashed line OR in Fig. 2.5 and is called 

 regular reflection. Whether or not the necessary compensation can be 

 achieved by such a front requires a more detailed examination but it is 

 clear that a front of the type indicated must be one of compression. 



The opposite extreme occurs if the medium above OB' offers no 

 resistance to compression. This state of affairs is very nearly realized 

 if the fluid below OB' is water and above OB' air, the ratio of compres- 

 sibilities being of the order 1/7 -10^ In this case it is not possible to 

 develop a significant compression in the medium along the boundary 



-^ ^ ->. ^ X. -^ ^ N X N ^ X ^ X 



u 



Uo«0 V' U = 



t;: 



|--r.- 



(a) Before Reflection (b)Afler Reflection 



Fig. 2.6 Normal reflection at a rigid boundary. 



OB', and pressure waves must be originated at which leave the fluid 

 along OB' in its original state of compression. There is of course no 

 opposition to motion of the boundary and hence no restriction on the 

 normal components of velocity. The necessary conditions are then 

 again conceivably realized by a pressure front originating at 0, but dif- 

 fering from the rigid boundary case, in that a rarefaction wave is re- 

 quired to reduce the pressure to its original value. In this case the 

 particle velocity developed by the rarefaction has a component toward 

 the boundary as indicated in Fig. 2.5. The fluid behind OR is there- 

 fore left with a normal component of velocity toward the boundary 

 which is the sum of the components introduced by the two pressure 

 fronts and the boundary will be displaced upward. 



In the special case w^here the boundary is normal to the incident 

 wave, incident and reflected wave fronts do not exist simultaneously. 

 If the boundary is perfectly rigid, the situation when the wave has just 

 reached it is one of fluid moving toward the boundary. This motion 

 can only be destroyed at the boundary by a discontinuity travelling 

 back through the moving fluid with intensity and velocity of such mag- 

 nitude as to destroy the flow velocity, and satisfy the Rankine-Hugoniot 



