Chapter 9. Instabilities

  1. Prof. Steven N. Shore

Published Online: 7 FEB 2008

DOI: 10.1002/9783527619054.ch9

Astrophysical Hydrodynamics: An Introduction, Second Edition

Astrophysical Hydrodynamics: An Introduction, Second Edition

How to Cite

Shore, S. N. (2008) Instabilities, in Astrophysical Hydrodynamics: An Introduction, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527619054.ch9

Author Information

  1. Dipartimento di Fisica ‘Enrico Fermi’, Università di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy

Publication History

  1. Published Online: 7 FEB 2008
  2. Published Print: 18 JUL 2007

ISBN Information

Print ISBN: 9783527406692

Online ISBN: 9783527619054

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Keywords:

  • astrophysical hydrodynamics;
  • instabilities;
  • waves;
  • convection;
  • pulsation;
  • thermal instability;
  • important instabilities

Summary

This chapter contains sections titled:

  • Introduction

  • Waves

    • Sound Waves as a Prototypical Instability

    • The Jeans Instability and Self-Gravitation: Density Waves on the Cheap

    • The Rotating Self-Gravitating Slab

    • The Jeans Instability and the Virial Theorem

    • Bifurcation for the First Time

    • Density Stratification: The Brunt–Väisälä Frequency and the Richardson Criterion

  • Convection

    • Incompressible Convection: The Rayleigh–Bénard Problem

    • Compressible Convection: Mixing Length Theory

      • A Brief Comment on Observational Consequences

    • Some Effects of a Magnetic Field

  • Pulsation as an Instability

    • The Hurwitz–Routh Criterion

    • Another Approach: Lagrangian Variational Method

  • Thermal Instability

  • A Selection of Important Instabilities

    • Rayleigh–Taylor Instability: Buoyancy and Density Discontinuities

    • Kelvin–Helmholtz Instability: Shear and Velocity Discontinuities

    • Shear Instability: Rayleigh Criterion for Velocity Gradients and, again, Boundary Layers

    • Taylor Instability: Rotation and Vorticity

    • The Magneto-Rotational Instability and Viscosity in Accretion Disks

  • Exeunt