# Book: All Things Flow - Fluid Mechanics for the Natural Sciences (Smyth)

- Page ID
- 18023

This book on fluid mechanics is concerned with phenomena that we have all been familiar with since childhood: flows you see in sinks and bathtubs, in rivers, and at the beach. In this context, we develop the mathematical techniques and scientific reasoning skills needed for higher-level courses and professional research. Prerequisites are few: basic linear algebra, differential and integral calculus and Newton’s laws of motion. As we go along we discover the need for the more advanced tools of tensor analysis.

The science of fluid mechanics is vast. Most books on the topic are concerned with technological applications, e.g., flow through pipes and machinery, that have little relevance in nature. But even among naturally occurring flows we cannot, and should not, try to cover everything. What I have done here is to identify three canonical flow structures that are common in nature: (1) vortices, (2) waves, and (3) hydraulic jumps.

- Front Matter
- 1: Introduction
- 2: Review of Elementary Linear Algebra
- 3: Cartesian Vectors and Tensors
- 4: Tensor Calculus
- 5: Fluid Kinematics
- 6: Fluid Dynamics
- 7: Vortices
- 8: Waves
- 9: Nonlinear, Hydrostatic Flow Over Topography
- 10: Postface
- 11: Exercises
- 12: Appendix A- Taylor Series Expansions
- 13: Appendix B- Torque and the Moment of Inertia
- 14: Appendix C- Isotropic Tensors
- 15: Appendix D- The Leva-Cevita Alternating Tensor
- 16: Appendix E- Vector Identities
- 17: Appendix F- The Cauchy Stress Tensor
- 18: Appendix G- Boussinesq Approximation
- 19: Appendix H- Bernoulli's Equation
- 20: Appendix I- Vector Operations in Curvilinear Coordinates
- 21: Appendix J- The Stokes Drift
- Back Matter

Thumbnail: Flowing water (Pixabay license; PublicDomainPictures via Pixabay)