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Introduction to Modeling Convection in Planets and StarsMagnetic Field, Density Stratification, Rotation$
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Gary A. Glatzmaier

Print publication date: 2013

Print ISBN-13: 9780691141725

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691141725.001.0001

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Density Stratification

Density Stratification

Chapter Twelve Density Stratification
Introduction to Modeling Convection in Planets and Stars

Gary A. Glatzmaier

Princeton University Press

This chapter examines the effects of large variations in density with depth, that is, density stratification. It first describes anelastic models for 2D cartesian box and 2D cylindrical annulus geometries, using entropy and pressure as working thermodynamic variables or using temperature and pressure, for both convectively unstable and stable regions. In particular, it considers anelastic approximation and how to formulate the anelastic equations, as well as the anelastic form of mass conservation, momentum conservation with entropy as a variable, internal energy conservation with entropy as a variable, and temperature as a variable. It also discusses possible choices for a reference state, focusing on polytropes, before explaining modifications to the numerical method and presenting the numerical simulations using the anelastic model.

Keywords:   density stratification, anelastic model, entropy, pressure, temperature, anelastic approximation, reference state, polytropes, numerical method, numerical simulations

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