Perturbation Analysis

Following Chevalier & Imamura (1982), we consider a perturbation

where is the perturbed velocity of the shock surface, taken to be real, and is the complex eigenvalue which determines the stability. (Hereafter, the subscripts ``0'' and ``1'' denote the steady state and the perturbed quantities respectively.) The time-dependent shock height is

where . We also assume that the perturbed variables are given by

where . Substituting equations (6), (7) and (8) into equations (1), (2) and (3) and considering the dimensionless variables , , , and , we obtain three complex, linear perturbed equations



and





where

Equations (9), (10) and (11) can be separated into six real decoupled linearised equations. With the boundary conditions, at the white dwarf surface, and , and at the shock surface (see Appendix B), the eigenvalues , and hence , can readily be obtained.

© Copyright Astronomical Society of Australia 1997