By Susan Friedunder (Eds.)
Friedlander S. An advent to the mathematical concept of geophysical fluid dynamics (NH Pub. Co., 1980)(ISBN 0444860320)
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Additional resources for An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics
E Choose a l l the << 1 and E << 1 By shining a l i g h t through t h e cylinder t h e alignment of the f i n e p a r t i c l e s w i l l make i t possible t o observe t h a t t h e e n t i r e column of f l u i d above the b a l l moves as though i t were r i g i d l y attached t o the b a l l . This e f f e c t is known a s a Taylor column. 24 A Taylor Column A Taylor Column FIGURE 2 Geostrophic flow 25 The explanation of t h i s phenomenon i s the following: cylinder has a r i g i d top perpendicular t o w component of v e l o c i t y is 0 k, a t t h e top.
V -m ] v2P+ 4 2 az 9 = 0. I n t h e case of the geostrophic approximation E = 0, and z. 7) reduces t o which is consistent w i t h t h e r e s u l t t h a t of 5 P i s independent The reduced i n v i s c i d equation i s n a t u r a l l y of lower 37 The Ekman l a y e r order and hence can not be used t o s a t i s f y boundary conditions on t h e t a n g e n t i a l , as well a s , the normal components of velocity. A s i s customarily the case i n a problem i n f l u i d dyna- mics, f r i c t i o n a l e f f e c t s must be included i f t a n g e n t i a l veloc i t y conditions a r e t o be s a t i s f i e d a t t h e boundary.
Hence the momentum equation has reduced t o a balance between C o r i o l i s force and the pressure gradient. peostrou balance of r o t a t i n g flow. 1) was derived a f t e r major s i m p l i f i c a t i o n s of the physics, however it gives a remarkably good d e s c r i p t i o n of t h e b a s i c behavior of a r o t a t i n g f l u i d and we w i l l use geostrophic flow as the fundamental s t a t e t o which we w i l l add physical complexities. 1) and ( 4 . 2 ) . TaKing t h e c u r l of ( 4 .
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)