Waves and Instabilities in the Atmosphere

Abstract

The theory of wave motions in a continuous media is one of the best-developed theories in classical fluid dynamics and special mathematical methods have been created for the purpose. A short review is given below Let δ(x, t)be a function of the distance x and time t and δ=ψ(x) at t = 0. Then, if at x = θ ± c t the equality

$$\delta = \psi (\theta ) = \psi (x\pm ct)$$

(1.1)

holds, this will mean that the initial profile ψ(x)moves in the positive or negative direction with velocity c preserving its shape. Evidently, a function of the type (1.1) is a solution of the one-dimensional wave equation ψ _tt = c ² ψ _xx .