Chapter 5. Similarity Methods

  1. Prof. Steven N. Shore

Published Online: 7 FEB 2008

DOI: 10.1002/9783527619054.ch5

Astrophysical Hydrodynamics: An Introduction, Second Edition

Astrophysical Hydrodynamics: An Introduction, Second Edition

How to Cite

Shore, S. N. (2007) Similarity Methods, in Astrophysical Hydrodynamics: An Introduction, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527619054.ch5

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;
  • similarity methods;
  • blast waves;
  • expanding ionization fronts;
  • static configurations;
  • polytropes;
  • classical gravitational collapse

Summary

This chapter contains sections titled:

  • Introduction

    • Blast Waves: The Sedov Problem

    • The Dimensionless Dynamical Equations

    • Stagnation Pressure

    • Snowplow Phase

    • Stellar Wind Bubble

    • Planetary Nebulae as a Special Case

  • Expanding Ionization Fronts

  • Similarity Methods for Static Configurations: Polytropes

    • The Lane–Emden Equation

    • From General Polytropes to the Isothermal Sphere

    • A Very Few Applications

  • Classical Gravitational Collapse

    • Pressureless Collapse

    • Isothermal Collapse: Effects of Pressure

  • Appendix: Diffusion Equations