By Susan Friedunder (Eds.)
Friedlander S. An creation to the mathematical thought 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
0 on the boundary l a y e r solu- t i o n c o r r e c t s f o r the behavior of the i n t e r i o r s o l u t i o n a t t h e wall. Let us denote Ekman boundary l a y e r q u a n t i t i e s by Since the Ekman l a y e r i s expansion of * P and * O(E1/‘) + G 1E l l 2 + + vlE lI2+ w 0 i &E l 1’2 + B, + PlE”2 + a - w = k = we consider an asymptotic i n powers of u = u0 a v = vo 1 a (”). ... ... 1) i n t h e EKman l a y e r where EV = + S u b s t i t u t i o n of t h e expan- O(E1’2). s i o n i n t o t h i s equation gives t o f i r s t order Now Po - O = - E - 1/2 0 as 5 - co Po Po hence .
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. the hence the normal I f the f l u i d above the b a l l were not t o move w i t h t h e b a l l t h e r e must be flow over t h e b a l l , and such a flow requires a non-zero component of v e l o c i t y w. However, the Taylor-Proudman w theorem t e l l s us t h a t t h e r e can be no v a r i a t i o n i n respect t o z = L z , hence it i s impossible t h a t and nonzero a t z = z ball.
Fresh S t i r the water uniformly u n t i l the water is i n r i g i d body r o t a t i o n . Cease t o s t i r and ob- serve and time the spin-down process. It is very easy t o follow the motion of the t e a leaves i f t h e d i s h is placed on a n overhead p r o j e c t o r and the experiment is projected onto a screen. It w i l l be seen t h a t the tea-leaves s p i r a l i n t o the c e n t e r of the d i s h w i t h reduced angular v e l o c i t y ; they ceaee t o move a f t e r a time s c a l e ’’‘ o(L/(n T h i s is, of vl/”)).
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)