Jump to ContentJump to Main Navigation
Introduction to Modeling Convection in Planets and StarsMagnetic Field, Density Stratification, Rotation$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 26 May 2022

Linear Stability Analysis

Linear Stability Analysis

Chapter Three Linear Stability Analysis
Introduction to Modeling Convection in Planets and Stars

Gary A. Glatzmaier

Princeton University Press

This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For this linear analysis, each Fourier mode n can be considered a separate and independent problem. The question that needs to be addressed now is under what conditions—that is, what values of Ra, Prandtl number Pr, and aspect ratio a—will the amplitude of the linear solution grow with time for a given mode n. This is a linear stability problem. The chapter first introduces the linear equations before discussing the linear code and explaining how to find the critical Rayleigh number; in other words, the value of Ra for a and Pr that gives a solution that neither grows nor decays with time. It also shows how the linear stability problem can be solved using an analytic approach.

Keywords:   linear stability analysis, critical Rayleigh number, linear code, Fourier mode, Prandtl number, aspect ratio, linear stability problem, linear equations

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.