Straight Characteristics and Particle Paths in a Simple Wave

Straight characteristics and particle paths in a simple wave. Piston path (P), straight characteristics (solid), and particle paths (dashed) are shown. 

Accdg to Ref 66, p 135 the usual way of treating shocks is to idealize them to jump discontinuities, in this way taking into account the effect of the irreversible process caused by friction and heat conditions. It is assumed that the flow involving such a discontinuous process is completely determin ed by the three lawstof conservation of mass, momentum and energy and the condition that the entropy does not decrease in the discontinuous process. Outside of the transition zone the flow is determined by the differential eqs 2.1.1, 2.2.2 2.2.3 listed on p 132 of Ref 66 

There are two types of discontinuity surfaces contact surfaces and shock fronts. There is no flow between regions separated by a contact surface, while shock fronts are crossed by the flow. A contact surface moves with the fluid and separates two zones of different density and temperature, but the same pressure. The normal component of the flow velocity is the same on both sides of a contact discontinuity 

If subscripts 0 and 1 refer to conditions on each side of discontinuity, the jump con ditions can be expressed by equations listed on p 136 of Ref 66 

It should be noted that the flow velocity relative to a shock is supersonic ahead and 

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