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)