P. Godon et G. Shaviv, THE DYNAMICS OF 2-DIMENSIONAL LOCAL AND FINITE PERTURBATIONS IN ENVELOPES OF ROTATING WHITE-DWARFS .1., The Astrophysical journal, 447(2), 1995, pp. 797-806
This is a first paper in a series in which we investigate the behavior
of two-dimensional local and finite perturbations in envelopes of sta
rs. In this paper we explore the dynamics of local and finite perturba
tions in an accreted envelope placed on a white dwarf. Viscosity and r
otation are included in a full two-dimensional Navier-Stokes system of
equations. A time-dependent Chebyshev method of collocation has been
developed and implemented for solving numerically the problem of the p
ropagation of perturbation in the envelope of a white dwarf. Our most
important result is that a local perturbation develops in two basic ph
ases: In phase A, which lasts about one dynamics timescale, the pertur
bation remains local. In phase B the perturbation expands all over the
star by means of pressure waves. Thus, a local perturbation becomes a
global one after about one dynamic timescale. The present calculation
s were carried out with a Reynolds number of 10(3) and 10(5) and we fi
nd that for these Reynolds numbers the viscosity (shear or turbulent)
has a minor effect on the development of the local perturbation into a
global one.