Turbulence in astrophysics: Stars

Turbulence is ubiquitous in astrophysics, ranging from cosmology, interstellar medium to stars, supernovae, accretion disks, etc. Large scales and small viscosities combine to form large Reynolds numbers. Because it is not possible in a single article to review all the above scenarios, we limit ourselves to stars, in which thermal instabilities give rise to turbulent convection as the dominant heat transport mechanism. (Accretion disks, where shear instabilities dominate the outward transport of angular momentum, will be the subject of a second article, planned for Volume 31.) Because of the lack of a satisfactory theory, turbulence constitutes a bottleneck that prevents astrophysical models from being fully predictive. Because continued use of phenomenological turbulence expressions would make astrophysical models perennially unpredictive, a way must be found to make astrophysical models as prognostic as possible. In addition to the difficulties brought about by turbulence, astrophysical settings introduce "malicious conditions," of which the most refractory to a satisfactory quantification are compressibility (caused by the large density excursions that characterize convective zones in stars) and rotation. Basic understanding of how they affect turbulence in general is still rather sketchy. Reasons for the choice of stars and accretion disks as prototype examples are the following: The underlying instabilities are very basic; laboratory and direct numerical simulations data help constrain theoretical models; and new observational data, especially from helioseismology, help discriminate among different models with unprecedented accuracy.