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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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Double-Diffusive Convection

Double-Diffusive Convection

Chapter:
Chapter Seven Double-Diffusive Convection
Source:
Introduction to Modeling Convection in Planets and Stars
Author(s):

Gary A. Glatzmaier

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691141725.003.0007

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 the “semiconvection” instability before discussing the possibility that the onsets of these instabilities at marginal stability have an amplitude that oscillates in time. The goal is to find the conditions that would result in a zero growth rate of the oscillation amplitude in order to determine the marginal stability constraint on the Rayleigh numbers for the onset of an oscillating instability. The chapter also shows how, after evolving beyond the onset of the instability, thermal diffusion between the moving parcel and the surroundings can alter the initial linear vertical profile of the horizontal-mean temperature into a “staircase” profile. This evolution of the temperature profile is investigated via nonlinear simulations.

Keywords:   double-diffusive convection, nonlinear evolution, salt-fingering instability, semiconvection instability, marginal stability, oscillating instability, thermal diffusion, staircase profile, temperature profile, nonlinear simulations

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