Chapter 3. Vorticity and Rotation

  1. Prof. Steven N. Shore

Published Online: 7 FEB 2008

DOI: 10.1002/9783527619054.ch3

Astrophysical Hydrodynamics: An Introduction, Second Edition

Astrophysical Hydrodynamics: An Introduction, Second Edition

How to Cite

Shore, S. N. (2007) Vorticity and Rotation, in Astrophysical Hydrodynamics: An Introduction, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527619054.ch3

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

SEARCH

Keywords:

  • astrophysical hydrodynamics;
  • vorticity;
  • rotation;
  • geostrophic approximation;
  • Rayleigh rotational stability criterion;
  • viscous effects;
  • self-gravitating bodies

Summary

This chapter contains sections titled:

  • Introduction

    • Coordinate Transformations

    • The Equations of Motion

    • Working in the Rotating Frame

    • Taylor–Proudman Theorem

    • The Barotropic Condition

    • Circulation and Kelvin's Theorem

    • Vortex Dynamics and Line Stretching

    • Magnus Force

  • Geostrophic Approximation

    • Rotation in an Incompressible Shallow Layer

    • The Rossby Number

    • The Ekman Layer

  • Rayleigh Rotational Stability Criterion

    • General Argument

    • Epicyclic Frequency

  • Viscous Effects: A Simple Example

  • Self-Gravitating Bodies

    • Baroclinicity

    • von Zeipel's Theorem for Rotating Self-Gravitating Bodies

    • Circulation Currents