On the fluid dynamics of evolving stars

The problem addressed is that of following the secular evolution of the velocity field and distribution of matter of a model star endowed with an arbitrary amount of angular momentum. A novel feature of the fluid dynamical formulation is the introduction and systematic use of material functions. These functions both facilitate the treatment of the free boun­dary of the star and enable one to use the circulation about certain contours as a priori constants of the motion. The equations governing the evolution of the material functions are adjoined to the Euler equations of fluid dynamics and are to be solved simultaneously with them. No special symmetry assumptions need to be imposed in formulating the equations. This makes it possible to apply them not only in the case of axisymmetric rotating stars, but also in the case of bar-shaped figures that may evolve toward double stars. The formulation is well adapted to the perturbation analysis needed in investigating bifurcation from families of slowly evolving fluid masses. The classes of model stars covered by the formulation include time dependent barotropic models, but are applicable to a significantly wider class of models as well. Even in the context of this wider, non-barotropic class of models, a restricted version of Kelvin’s circulation theorem holds, and plays a major role in rendering determinate the equations of secular evolution.