Results of detailed computer simulations of mass loss from a cataclysmic variable secondary are presented. The calculations involve solution of the nonlinear hydrodynamical equations of stellar structure under varying degrees of approximation in an attempt to determine stability of the mass loss process. For comparison with previous theoretical studies dynamical sequences were computed assuming spherically symmetric mass loss from the secondary. The assumption of spherical symmetry is very poor since nearly all of the transferred material is lost within a small region about the inner Lagrangian point. Dynamical sequences treating only the region near the Lagrangian point were constructed in a manner consistent with the assumption of Roche geometry. Finally the effects of mass flow nonorthogonal to the Roche equipotential surfaces were treated in a very simple way. The last generalization produces stable mass loss in a model which was unstable for the less realistic approximation schemes. The finding of stable mass transfer implies that instability of the secondary star is not the mechanism leading to cataclysmic variable outbursts. This conclusion is consistent with published observations of dwarf novae made just prior to outburst.

The rapid coherent oscillation during a dwarf nova outburst is attributed to an accretion-driven wave going around the white dwarf component of the binary system. The increase and decrease in the period of this oscillation is due to the change in the velocity of the wave as it is first being driven and then damped. Qualitatively, a large number of observations can be explained with such a model. The beginnings of a mathematical representation of this model are developed.

The degeneracy of frequencies of nonradial oscillations is resolved in the presence of rotation. As observed in an inertial frame the frequency of a nonradial oscillation in a uniformly rotating star is given as

The linear adiabatic oscillations of a uniformly rotating star are examined with respect to a co-rotating frame of reference. It is shown that time-independent displacement fields are allowed and can be represented as toroidal fields. The time-dependent oscillation modes are governed by a system of differential equations of the fourth order in time for axisymmetri’c perturbations, and of the fifth order for non-axisymmetric perturbations. Therefore, in comparison to a non-rotating spherical star, a rotating star allows a new class of non-axisymmetric oscillation modes with non-zero frequencies. These modes correspond to the r-modes, which originate from purely toroidal displacement fields in a non-rotating spherical star.

The perturbation problem that describes the effect of a weak magnetic field on stellar adiabatic oscillation is considered. This perturbation problem is singular when the magnetic field does not vanish at the stellar surface, and a regular perturbation scheme fails where the magnetic pressure is comparable to the thermodynamic pressure. The application of the Method of Matched Asymptotic Expansion is used to obtain expressions for the eigenfunctions and the eigenfrequencies.

α-stability analysis is used to investigate the adiabatic stability of a star containing an axisymmetric toroidal magnetic field. Necessary and sufficient conditions for α-stability are derived. Special attention is devoted to the typical hydromagnetic instabilities that can be introduced by a weak toroidal magnetic field in a star that is stably stratified in the absence of any magnetic field. An expression for the maximum growth rate of instability is derived and the basic properties of the displacement fields associated with the instabilities are indicated.