Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations

Abstract

Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here we study the properties of gravity waves in stably-stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably-stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.

Accepted for publication in ApJ. 20 pages emulateapj format, 7 figures

References in corpus (11)

• Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope
• Persistent Magnetic Wreaths in a Rapidly Rotating Sun
• Structure and Evolution of Giant Cells in Global Models of Solar Convection
• Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance
• Magnetic Cycles in a Convective Dynamo Simulation of a Young Solar-type Star
• Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations
• Simulations of core convection in rotating A-type stars: Magnetic dynamo action
• Rapidly Rotating Suns and Active Nests of Convection
• Numerical Simulations of Penetration and Overshoot in the Sun
• Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution
• Nonlinear Dynamics of Gravity Wave Driven Flows in the Solar Radiative Interior

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• The Breakdown of the Anelastic Approximation in Rotating Compressible Convection: Implications for Astrophysical Systems