Variational Formulation of Fluid and Geophysical Fluid Dynamics

Mechanics, Symmetries and Conservation Laws

  • Gualtiero Badin
  • Fulvio Crisciani

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Gualtiero Badin, Fulvio Crisciani
    Pages 1-55
  3. Gualtiero Badin, Fulvio Crisciani
    Pages 57-106
  4. Gualtiero Badin, Fulvio Crisciani
    Pages 107-133
  5. Back Matter
    Pages 183-218

About this book


This book describes the derivation of the equations of motion of fluids as well as the dynamics of ocean and atmospheric currents on both large and small scales through the use of variational methods. In this way the equations of Fluid and Geophysical Fluid Dynamics are re-derived making use of a unifying principle, that is Hamilton’s Principle of Least Action. The equations are analyzed within the framework of Lagrangian and Hamiltonian mechanics for continuous systems. The analysis of the equations’ symmetries and the resulting conservation laws, from Noether’s Theorem, represent the core of the description. Central to this work is the analysis of particle relabeling symmetry, which is unique for fluid dynamics and results in the conservation of potential vorticity. Different special approximations and relations, ranging from the semi-geostrophic approximation to the conservation of wave activity, are derived and analyzed. Thanks to a complete derivation of all relationships, this book is accessible for students at both undergraduate and graduate levels, as well for researchers. Students of theoretical physics and applied mathematics will recognize the existence of theoretical challenges behind the applied field of Geophysical Fluid Dynamics, while students of applied physics, meteorology and oceanography will be able to find and appreciate the fundamental relationships behind equations in this field.


Quasi-Geostrophic Model Conservation of vorticity Particle labelling symmetry Nonlinear geophysical fluid dynamics Physical and mathematical oceanography

Authors and affiliations

  • Gualtiero Badin
    • 1
  • Fulvio Crisciani
    • 2
  1. 1.Universität HamburgHamburgGermany
  2. 2.University of TriesteTriesteItaly

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Earth and Environmental Science
  • Print ISBN 978-3-319-59694-5
  • Online ISBN 978-3-319-59695-2
  • Series Print ISSN 1866-8348
  • Series Online ISSN 1866-8356
  • Buy this book on publisher's site