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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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Nonlinear Finite-Amplitude Dynamics

Nonlinear Finite-Amplitude Dynamics

Chapter:
Chapter Four Nonlinear Finite-Amplitude Dynamics
Source:
Introduction to Modeling Convection in Planets and Stars
Author(s):

Gary A. Glatzmaier

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691141725.003.0004

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After explaining the modifications to the linear model, the chapter shows how to add the nonlinear terms to the code. It also discusses the Galerkin method, the strategy of computing the contribution to the nonlinear terms for each mode due to the binary interactions of many other modes. The Galerkin method works fine as far as calculating the nonlinear terms is concerned because of the simple geometry and convenient boundary conditions. The chapter concludes by showing how to construct a nonlinear code and performing nonlinear simulations.

Keywords:   numerical code, nonlinear terms, finite-amplitude simulations, Galerkin method, spectral space, linear model, boundary conditions, nonlinear code, nonlinear simulations

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