Variational Formulation of Fluid and Geophysical Fluid Dynamics: Mechanics, Symmetries and Conservation Laws (Advances in Geophysical and Environmental Mechanics and Mathematics) - Softcover

Badin, Gualtiero; Crisciani, Fulvio

Softcover

ISBN 10: 3319866818 ISBN 13: 9783319866819

Publisher: Springer, 2018

Synopsis

Emphasizes a subject matter of interdisciplinary interest for meteorology, oceanography, physics and applied mathematics

Provides a detailed derivation of the equations of motion from conserved quantities and from system symmetries

Focuses in particular on the analysis and consequences of particle relabeling symmetry

Applies results to different approximations, such as the semi-geostrophic equations, and different relations, such as the conservation of wave activity

About this title

About the Author

Dr. Gualtiero Badin is professor at the Universität Hamburg (Germany). He is specialized in geophysical fluid dynamics, ocean dynamics, especially at frontal scales, geostrophic turbulence and nonlinear dynamics.

Dr. Fulvio Crisciani is lecturer at the University of Trieste (Italy). He has more than 32 years experience in oceanography and is specialized in geophysical fluid dynamics and the climate of the gulf of Trieste.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2018
• Language: English
• ISBN 10: 3319866818
• ISBN 13: 9783319866819
• Binding: Paperback
• Number of pages: 236