An Introduction to the Mathematical Theory of Geophysical by Susan Friedunder (Eds.)

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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Example text

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).

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