Examples from Fluid Mechanics
In this chapter we consider some examples from fluid mechanics with the aim of illustrating the derivation of approximate equations, the role of several small parameters, and the calculation of uniformly valid results. Strictly speaking, there is no difference with the material discussed in Chapter 4. The emphasis here is on applications, so that we will not be dealing with model equations, but rather with nonlinear systems which reduce in the first approximation to some well known equation such as the transonic equation or the Korteweg-de Vries equation, etc. Typical to many problems is the occurrence of several small parameters. We will show how one must specify certain relations between these small parameters to account systematically for various competing perturbation terms and to derive meaningful approximations.
KeywordsShock Wave Fluid Mechanics Boussinesq Equation Hydraulic Jump Transonic Flow
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