Lighthill Waves In Fluids.pdf
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The fourth chapter deals with non-linear dispersive waves. Theanalysis is restricted to the case of a fluid with constantviscosity, and takes up the fundamental problem of three-dimensionallinear non-dispersive waves. The analysis is fairly straight-forwards, and some features of the analysis areof interest to marine engineers.
The second chapter is concerned with sin-gle-frequency harmonic waves, and the analysis extends to inharmonic waves. The analysis is carried out to first order in adiabatic index, and this is shown to be a useful approximation for the most important effect of non-linearity - the development of coupling between waves of differentmodes. The chapter also shows how non-linearity affects wave-motion in a shallow layer of water. Here, waves are shown to grow and decay in dif-ferent ways as the wave-height varies, and the importance of this forthe design of wave buoys is discussed. The third chapter deals withthe coupled behaviour of the surface waves and geostrophic current-waves, and here we find the first mention of a governing equation for the relative motionof these two types of wave. This is a vital subject in manypractical problems, particularly when the surface waves are non-dispersive (as here) and the geostrophic current-waves aredispersive.
The second chapter examines the dynamics of gravity waves. Theseare the waves of most interest to marine engineers,and it is here that we find some of the most interesting developmentsin the theory. Here, we find the important analysis of linearand non-linear waves in two dimensions, where the analysis issimilar to the theory of waves on a plate. Although this chapter isafoot-while chapter 3 deals with the three-dimensional ocean waves,it is the next chapter that is the most useful to the marineengineer.
Excluding the epilogue, there are three chapters on thesubject of Waves in Fluids. These cover, in a fairly briefform, the propagation of waves in two- and three-dimensions, inhomogeneous fluids, and, finally, waves in dispersive media.
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