By Susan Friedunder (Eds.)
Friedlander S. An creation to the mathematical idea 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
Tr I I I I / / \ I \ I I \ \ \ \ \ \ \ \ \ / \ \ \ \ \ \ \ / / \ \ I I I I I Spin-up c i r c u l a t i o n FIGURE 9 We can describe spin-up i n physical terms i n the example of a cylinder where the boundary v e l o c i t y i s increased from to n(l+c). n After a couple of revolutions Ekman l a y e r s form on the upper and lower boundaries. The f l u i d i s spun rapidly outwards and f r i c t i o n a l forces allow the angular v e l o c i t y t o increase. ior. A small v e r t i c a l v e l o c i t y i s induced i n the i n t e r - We can consider the Ekman layer a s "sucking in" f l u i d 51 The Ekman l a y e r from the i n t e r i o r t o replace the f l u i d t h a t i s spun r a d i a l l y outward.
P(x,y) w i l l satisfy It w i l l then be necessary t o i n t r o - . Geos t rophic flow 23 duce more physics ( s e e Chapter 5 ) t o determine which twodimensional pressure P(x ,y) describes a p a r t i c u l a r problem: once t h i s is done the geostrophic r e l a t i o n s ( 4 . 4 ) immediately determine the h o r i z o n t a l v e l o c i t y . -3 An i n t e r e s t i n g and f a i r l y e a s i l y observed phenomenon t h a t can be explained using t h e Taylor-Proudman theorem is t h e Taylor Column.
This experiment is only an approximation t o t h e o r e t i c a l spin-down s i n c e the perturbation of the boundary v e l o c i t y is not small, i n f a c t , t h e Rossby number E = 1, hence the non- 53 The EKman l a y e r l i n e a r terms can not s t r i c t l y be neglected. However, the experiment does produce a spin-down time t h a t i s remarkably c l o s e t o the predicted value. We note t h a t t h e phenomena of spin-up o r spin-down of a f l u i d t h a t i s i n i t i a l l y i n r o t a t i o n a r e equivalent ( i n t h e l i n e a r theory).