1. Dynamic Similarity http://www.typefree diabetes.com/Article s.asp?ID=150 http://www.eosnap.com/?tag=strait-of-gibraltar Dimensionless Science

2. Ideas needed to perform Dimensional Analysis All terms in equation must have same dimensions Terms in equation can be expressed with 3 basic dimensions: Mass, Length, Time Dimensions of these variables can be arranged in “Dimensional Matrix”

3. Dimensional Matrix The rank r of a matrix is the size of the largest square submatrix with non-zero determinant r = 3 Most problems in fluid mechanics Buckingham’s PI theorem: “n variables can be combined to form exactly (n-r) independent non-dimensional variables.”

4. inertial vs viscous Reynolds Number

5. Low Re High Re Flow is laminar when Re < 1000 Flow is in transition to turbulence when 100 < Re < 10 5 to 10 6 Flow is turbulent when Re > 10 6, unless the fluid is stratified

6. Consider an oceanic flow where U = 0.1 m/s; L = 10 km; kinematic viscosity = 10 -6 m 2 /s Is friction negligible in the ocean?

7. inertial vs pressure Froude Number

8. http://www.yourlocalweb.co.uk/greater-manchester/city-of-manchester/higher-blackley/pictures/

9. pressure vs inertial Euler Number

10. http://www.freefoto.com/browse/1222-02-0?ffid=1222-02-0 Great Fountain Geyser, Yellowstone National Park, USA

11. http://ya.astroleague.org/?p=1445

12. local vs inertial Strouhal Number f = frequency of motion; A = amplitude of motion – for flying or swimming organisms (fin or wing)

13. Taylor at al. (2003, Nature 425, 707-711(16 ) doi:10.1038/nature02000) http://www.nature.com/nature/journal/v425/n6959/fig_tab/nature02000_F1.html#figure-title “Left panels, root-flapping motion; right panels, heaving motion. Amplitude, twice wing chord; static angle of attack, 15°; flow speed, 1.5 ms -1 ; smoke wire visualizations made at end of downstroke. a, For St < 0.10, flow separates at the sharp leading-edge, but no discrete vortex forms. b, For 0.10 < St < 0.25, a leading-edge vortex forms but is shed before the downstroke ends. c, For 0.25 < St < 0.45, the leading-edge vortex is shed as the downstroke ends. d, For St > 0.45, trailing edge separation produces a characteristic mushroom- shaped wake. At higher St, the wing collides with shed vorticity on the upstroke, giving an energetically inefficient mode.”

14. Dynamic Similarity http://www.typefree diabetes.com/Article s.asp?ID=150 http://www.eosnap.com/?tag=strait-of-gibraltar