Instructive Observations, Experiments and Theory in Fluid Dynamics

Vortices

• Flow behind airfoil
• Polar Low in North Atlantic Ocean

Density Stratified Media

• Atmospheric Inversion
• Inversions and Plumes

Waves

• Surface Waves
• Breaking Surface Waves
• Dead Water
• Three Layer Flow
• 1-Layer Flow over Obstacle
• 2-Layer Flow over Obstacle
• 2-Layer Non-Hydrostatic Flow over Obstacle
• Continuously Stratified Flow over Obstacle
• Internal Wave Breaking Behind Obstacle

Hydraulic Jumps, Bores and Gravity Currents

• Hydraulic Jump
• Undular and Turbulent Bores

Convection and Plumes

• Rayleigh-Taylor Instability
• Double Diffusive Convection
• Rayleigh Number
• Critical Rayleigh number
• Rotating Convection
• Plumes in Inversion
• Plumes in Rotating Environment

Turbulence

• Effective Viscosity of Turbulence
• Scaling in Turbulence
• Symmetry in Turbulence
• Turbulence in Atmospheric Front
• Spectra of Atmospheric Turbulence
• Collapse of Stratified Turbulence

Shock Waves

• Picture of shock wave surround fighter jet
• MPG Movie of shock wave surround fighter jet (1.4MB)
• For more detailed explanations, follow the links from http://www.wilk4.com/misc/soundbreak.htm

Miscellaneous Principles and Applications of Mathematics

General

• Properties of Even and Odd functions
• Deriving Useful Trigonometric Identities using Euler's Formula

Integrals

• Parametric representation of line and surface integrals
• Fundamental Theorem of line integrals, Green's Theorem, Stokes' Theorem and Divergence Theorem
• Useful Integrals of Trigonometric Functions which come up when evaluating Fourier Series Coefficients
• Table of Zeroes and Integrals of Bessel Functions
• Technique of Differentiating through Integral

Fourier and Bessel Series

• Convergence of Fourier Sine Series
• Image filtering using Discrete Fourier Transforms
• Table of Fourier series and their coefficients
• Convergence of Bessel functions

Special Functions

• Bessel functions: J0 and Y0
• Asymptotic approximations to J0
• Bessel eigenfunctions: J0(a r)
• Bessel functions: Jn
• modified Bessel functions: I0 and K0
• Table of Zeroes and Integrals of Bessel Functions
• Table Special Functions (trig/Bessel/Legendre/Hermite) and their Properties

Partial Differential equations

• Flowchart describing steps in solution of a partial differential equation using separation of variables and orthogonality of special functions
• Convergence of Series Solution to heated plate problem
• Table of Series Solutions to 1D wave and heat equation and to the 2D potential equation in Cartesian co-ordinates

Acknowledgements and References

Some of the pictures have been generously provided by:

• Graham Hughes, Australian National University
• Adarsh Mehta, University of California, San Diego

Images of classic experiments appear in

• "Illustrated Experiments in Fluid Mechanics", The NCFMF Book of Film Notes, MIT Press (1972)

Some images have been reproduced from journal articles and web pages:

• Fritts and Nastrom, J. Atmospheric Sciences
• B. Fryxell, GSFC NASA
• S. Sakai, Kyoto University

Department of Physics

Department of Earth & Atmospheric Sciences