ABSTRACT
The introductory chapter has basic definitions of a wave, basic equations of motion, different conservation laws, the concept of phase and group velocities, and the resulting notion of dispersion relation. Chapters 2 and 3 deal with waves in electromagnetic fields and the different modes in an uniform media. In this chapter, for the first time, we shall discuss waves and oscillations in fluids (both liquids and gases). We shall discuss different types of waves in fluids, depending on the geometry and the external forces acting on them. To begin we shall concentrate mostly on waves in liquids. In particular, we shall deal with incompressible fluids. The different sections in the chapter will include discussion on small amplitude waves, the study of waves in
water under the influence of gravity, linear capillary and gravity waves, and surface waves. The derivation of Klein−Gordon and Boussinesq equations is mentioned briefly. The concept of shallow water waves (the depth of the layer being smaller than the wavelength of the wave) is discussed in detail. We will also discuss nonlinear effects of the otherwise small amplitude waves.The special case of plane waves in a layer of constant depth is dealt with briefly. We shall present some examples as applicable to geophysical fluid dynamics (Poincare´, Kelvin, inertial waves). Application of Rayleigh and Lamb waves to hydrodynamics and soil mechanics is mentioned in passing. Waves which have large wavelengths have to be discussed in a rotating frame. Thus, we shall discuss waves, both in nonrotating as well as rotating systems.
