Improved Sound-proof Treatments of Fluid Dynamics in Stellar Interiors
American Astronomical Society, AAS Meeting #221, #158.01
Published in Jan 2013
Plasma flows in deep stellar interiors are typically much slower than the local speed of sound. Owing to this, simulations of stellar convection and dynamo action typically employ various "sound-proof" equations, which filter the fast sound waves but can follow the subsonic convective flows. These sound-proof equations include the anelastic equations, which typically are derived in adiabatically-stratified stellar convection zones, and the pseudo-incompressible equations. In stars like the Sun, the radiative zone underlying the convection zone is a region of stable subadiabatic stratification, where motions remain highly subsonic and gravity waves dominate the dynamics. Sound-proof equations filter sound waves by imposing additional constraints on the fluid equations. If the momentum equation is not consistent with the additional constraints, the equations violate energy conservation in stratified atmospheres. Using a consistent Lagrangian approach we derive energy conserving sound-proof equations and study applications of sound-proof equations to dynamics in stellar radiative zones. We find that some formulations fail to conserve energy in regions of stable stratification and instead conserve a stratification weighted pseudo energy. Dynamics in the non-energy-conserving systems are incorrectly captured. We provide a mapping to equations that do conserve energy and discuss gravity wave dynamics in stably-stratified stellar regions in the context of stars more massive than the Sun, where overshooting convection drives gravity waves in the overlying radiative envelope.
(c) 2013: American Astronomical Society