Project goal

We rigorously construct stellar wind solutions to the Navier-Stokes equations, incorporating temperature-dependent viscocity and heat conduction, using methods from geometric singular perturbation theory. This project resulted in my first ever first-author paper. :)

Collaborator

Paul Carter.

Abstract

The one-fluid stellar wind problem for steady, radial outflow is considered, including effects of heat conduction and viscosity. The associated nondimensionalized equations of conservation of mass, momentum, and energy are singularly perturbed in the large Reynolds number limit, and stellar wind profiles are constructed rigorously in this regime using geometric singular perturbation techniques. Transonic solutions, which accelerate from subsonic to supersonic speeds, are identified as folded saddle canard trajectories lying in the intersection of a subsonic saddle slow manifold and a supersonic repelling slow manifold, returning to subsonic speeds through a viscous layer shock, the location of which is determined by the associated far-field boundary conditions.

Keywords: stellar wind – canards – geometric singular perturbation theory

Publication

A. M. Bauer, P. Carter. Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction. SIAM Journal on Applied Dynamical Systems, 20(1), 2021. https://doi.org/10.1137/20M1314240