ESS227
Prof. Jin-Yi Yu
Purpose
of Perturbation Method
•If terms that are products of the perturbation variables
are neglected, the nonlinear
governing equations are reduced to linear differential equations in the perturbation variables in which the
basic state variables are specified
coefficients.
•These equations can then be solved by standard methods
to determine the character
and structure of the perturbations in terms of the known basic state.
•For equations with constant coefficients the solutions
are sinusoidal or exponential
in character.
•Solution of perturbation equations then determines such
characteristics as the
propagation speed, vertical structure, and conditions for growth or decay of the waves.
•The perturbation technique is especially useful in
studying the stability of
a given basic state flow with respect to small superposed perturbations.