2. Waves of Finite Amplitude

The propagation of waves of finite amplitude and the change in wave profile leading to the formation of shock waves is the subject matter of this chapter. Simple examples of piston motion are presented to illustrate the formation of a normal shock wave and the time and place for its formation are also discussed. A brief introduction to Riemann invariants and the method of characteristics is presented and some examples to illustrate the method of characteristics in solving partial differential equations are outlined. The solution of nonlinear equations that result in the characteristics intersecting and the formation of shock waves are illustrated. The chapter concludes with some examples to illustrate the application of the method of characteristics and Riemann invariants to simple flow problems involving piston motion.