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Print Price: $36.50

Format:
Paperback
304 pp.
30 grayscale line figures, 171 mm x 246 mm

ISBN-13:
9780198805038

Publication date:
October 2018

Imprint: OUP UK

Fluid Mechanics

A Geometrical Point of View

S. G. Rajeev

Fluid Mechanics: A Geometrical Point of View emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to fluid mechanics. This follows on from the author's book Advanced Mechanics (Oxford University Press, 2013).

After introducing the fundamental equations (Euler and Navier-Stokes), the book provides particular cases: ideal and viscous flows, shocks, boundary layers, instabilities, and transients. A restrained look at integrable systems (KdV) leads into a formulation of an ideal fluid as a hamiltonian system. Arnold's deep idea, that the instability of a fluid can be understood using the curvature of the diffeomorphism group, will be explained. Leray's work on regularity of Navier-Stokes solutions, and the modern developments arising from it, will be explained in language for physicists.

Although this is a book on theoretical physics, readers will learn basic numerical methods: spectral and finite difference methods, geometric integrators for ordinary differential equations. Readers will take a deep dive into chaotic dynamics, using the Smale horse shoe as an example. Aref's work on chaotic advection is explained. The book concludes with a self-contained introduction to renormalization, an idea from high energy physics which is expected to be useful in developing a theory of turbulence.

Readership : Advanced undergraduate and beginning graduate students in theoretical physics, researchers and engineers interested in general principles, and mathematicians looking for applications.

1. Vector Fields
2. Euler's Equations
3. The Navier-Stokes Equations
4. Ideal Fluid Flows
5. Viscous Flows
6. Shocks
7. Boundary Layers
8. Instabilities
9. Integrable Models
10. Hamiltonian Systems Based on a Lie Algebra
11. Curvature and Instability
12. Singularities
13. Spectral Methods
14. Finite Difference Methods
15. Geometric Integrators

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S. G. Rajeev was born in Trivandrum, India. He has a B.Sc. degree from the University of Kerala and a Ph. D. from Syracuse University. After a stint as a Postdoctoral Fellow at MIT, he has been on the faculty at the University of Rochester, where he is a Professor of Physics and of Mathematics. He has done research on several topics in high energy physics and quantum gravity: soliton models for hadrons, string theory, renormalization, quantum field theory, and Yang-Mills theories - but fluid mechanics was his first love.

Making Sense - Margot Northey and Joan McKibbin
The Lattice Boltzmann Equation - Dr. Sauro Succi
Introduction to Microfluidics - Dr. Patrick Tabeling

Special Features

Connects fluid mechanics to theoretical physics, allowing the application of powerful ideas from other areas of physics.
Geometric tools allow for deeper understanding.
Includes Lie theory, a powerful mathematical tool used in fundamental physics.
Discussion of dynamical systems connects fluid mechanics to chaos theory.