Analytic Formalism of 3-D Unstable Linear Wave Packets.

Abstract

The analytic formalism for studying absolute and convective instabilities and spatially amplifying waves in 3-D flows of general nature is developed. The criterion by which a point (k, l, omega) in the wave number-frequency space contributes to the instability is fomulated in terms of the dispersion relation function D (k, l, omega) of the problem. Consequently, the causality condition for spatially amplifying waves is obtained. A procedure for finding a direction of maximal spatial amplification is presented. Application of the technique to computing the N-factor in the e exponent N method is discussed.