Fluid Dynamics
Table of Contents
1. Overview
The Reynolds number measures how unimportant viscosity is, by taking the ratio of non-viscous forces to viscosity. For the atmosphere, around 100km altitude and below, the Reynolds number is usually huge, so viscosity is unimportant. What's more important is the turbulence (source; ch 8 "The Planetary Boundary Layer" of John Holton's Introduction to Dynamic Meteorology).
Liquids are (usually) incompressible fluids.
Gases are (usually) compressible fluids.
See also further topics on fluids.
I have collected some notes in a separate blog, though I haven't written anything lately.
2. Euler Fluid
For inviscuous fluid, we use Euler's equations for the equations of motion. This is really a sort of nonlocal Poisson equation.
- Peter Constantin,
"The Euler equations and nonlocal conservative Riccati equations".
International Mathematics Research Notices 2000 no.9 (2000) pp.455–465 Pages 455–465, doi:10.1155/S1073792800000258 Eprint - Peter Constantin,
"On the Euler Equations of Incompressible Fluids".
Bulletin of the AMS 44 no.4 (2007) pp.603–621 PDF and Eprint - P. Constantin,
"Euler equations, Navier-Stokes equations and turbulence".
PDF - C. Bardos, E. Titi,
"Euler equations of incompressible ideal fluids".
PDF
3. References
- Stephen Childress,
"An Introduction to Theoretical Fluid Dynamics".
Lecture notes, pdf, 177 pages. - Alexandre Chorin, Jerrold Marsden,
A Mathematical Introduction to Fluid Mechanics.
Third ed., Springer, 1993. - Landau and Lifshitz,
Fluid Mechanics.
Second ed., Butterworth-Heinemann, 1987. This is my primary reference. - Simon J.A. Malham,
"Introductory fluid mechanics".
Lecture notes pdf, 2014, 74 pages.
3.1. Recommendations/Lookup
- George Batchelor,
An Introduction to Fluid Dynamics.
Cambridge University Press, 2000.- Remark: this seems to be the basis of several modern texts on fluids, like Malham's lecture notes or Childress's book; but this may be because there are only finitely many ways to present the material.
- Laurent Schoeffel,
"Lectures on Fluid Dynamics".
Eprint arXiv:1407.3162. - CFD Python: 12 steps to Navier-Stokes Lorena A. Barba Group
- Tai-Peng Tsai,
Lectures on Navier-Stokes Equations.
AMS Publishers.