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Title: ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. II. LAGRANGIAN CONSTRAINED ANALYSIS

The speed of sound greatly exceeds typical flow velocities in many stellar and planetary interiors. To follow the slow evolution of subsonic motions, various sound-proof models attempt to remove fast acoustic waves while retaining stratified convection and buoyancy dynamics. In astrophysics, anelastic models typically receive the most attention in the class of sound-filtered stratified models. Generally, anelastic models remain valid in nearly adiabatically stratified regions like stellar convection zones, but may break down in strongly sub-adiabatic, stably stratified layers common in stellar radiative zones. However, studying stellar rotation, circulation, and dynamos requires understanding the complex coupling between convection and radiative zones, and this requires robust equations valid in both regimes. Here we extend the analysis of equation sets begun in Brown et al., which studied anelastic models, to two types of pseudo-incompressible models. This class of models has received attention in atmospheric applications, and more recently in studies of white-dwarf supernova progenitors. We demonstrate that one model conserves energy but the other does not. We use Lagrangian variational methods to extend the energy conserving model to a general equation of state, and dub the resulting equation set the generalized pseudo-incompressible (GPI) model. We show that the GPI equations suitably capturemore » low-frequency phenomena in both convection and radiative zones in stars and other stratified systems, and we provide recommendations for converting low-Mach number codes to this equation set.« less
Authors:
;  [1] ; ;  [2] ;  [3]
  1. Department of Astronomy and Theoretical Astrophysics Center, University of California Berkeley, Berkeley, CA 94720 (United States)
  2. Department of Astronomy, University of Wisconsin, Madison, WI 53706-1582 (United States)
  3. Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA (United States)
Publication Date:
OSTI Identifier:
22130939
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 773; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; ENERGY CONSERVATION; EQUATIONS OF STATE; GRAVITY WAVES; LAGRANGIAN FUNCTION; MACH NUMBER; ROTATION; SOUND WAVES; VARIATIONAL METHODS; WHITE DWARF STARS