Theoretical Fluid Mechanics

Author:            Richard Fitzpatrick

Publisher:         IOP Publishing

Publication Date:  December, 2018

ISBN:              978-0-7503-1552-4

Nowadays, physics departments in the United States of America rarely offer courses in fluid mechanics. This unfortunate state of affairs has arisen partly because fluid mechanics research mostly takes place in engineering and applied mathematics departments, and partly because the significant shrinkage in the numbers of physics faculty, due to death and retirement, that has taken place over the last decade makes it increasingly difficult for physics departments to offer courses that are not regarded at central components of the physics curriculum (as, unfortunately, is the case with fluid mechanics). The only viable alternative for physics students who wish to learn fluid mechanics from a physics point of view is self-study.

This book has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. The book is, therefore, fairly comprehensive, completely self-contained (in that, the equations of fluid mechanics are derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix), and is accompanied by about 180 exercises with completely worked-out solutions. The book also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model.

The title of this book, Theoretical Fluid Mechanics, is meant to indicate that the book avoids empirical and semi-empirical approaches to fluid mechanics, and, instead, concentrates on that subset of fluid behavior that can be treated exactly. The book is also restricted to classical, Newtonian, isotropic, and non-relativistic fluids.

1. Mathematical Models of Fluid Motion.

2. Hydrostatics.

3. Surface Tension.

4. Incompressible Inviscid Flow.

5. Two-Dimensional Incompressible Inviscid Flow.

6. Two-Dimensional Potential Flow.

7. Axisymmetric Incompressible Inviscid Flow.

8. Incompressible Boundary Layers.

9. Incompressible Aerodynamics.

10. Incompressible Viscous Flow.

11. Waves in Incompressible Fluids.

12. Terrestrial Ocean Tides.

13. Equilibrium of Compressible Fluids.

14. One-Dimensional Compressible Inviscid Flow.

15. Two-Dimensional Compresible Inviscid Flow.

A. Vectors and Vector Fields.

B. Cartesian Tensors.

C. Non-Cartesian Coordinates.

D. Ellipsoidal Potential Theory.

E. Calculus of Variations.