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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.

Last Updated: Mon, 24 Apr 2023 09:16:49 -0700