Book Description

The stability to small perturbations of shear layer and jet flows (z) in atmospheres with potential temperature (z) is investigated. The problem is reduced to a chardcteristic value problem for the dimensionless wave frequency v which appears in a second-order differential equation with the dependent variable being the horizontal and temporal Fourier transform amplitude of the vertical component of the perturbation momentum vector. Broken-line profiles of E(z) and (z) are used in the analysis of this problem. Integral equations, over the domain of the fluid, which contain both quadratic forms and interfacial contributions, are derived. The interfacial terms vanish for continuous flows, and the theorems of Synge, Howard, and Miles follow. A necessary and sufficient condition for instability is also obtained for continuous flows; however, its usefulness is compromised by integrands which depend on both the basic state flow and the dependent variable of the governing differential equation.