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Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Gary A. Glatzmaier

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of ... More


A Model of Rayleigh-Bénard Convection

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, ... More


Numerical Method

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. ... More


Postprocessing

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ... More


Internal Gravity Waves

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on internal gravity waves in a stable thermal stratification. When the amplitude of the fluid velocity is small relative to the amplitude of the phase velocity, a linear ... More


Double-Diffusive Convection

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then ... More


Time Integration Schemes

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer ... More


Spatial Discretizations

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It ... More


Boundaries and Geometries

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude ... More


Magnetic Field

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0011
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first ... More


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