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

By Susan Friedunder (Eds.)

Friedlander S. An creation to the mathematical conception of geophysical fluid dynamics (NH Pub. Co., 1980)(ISBN 0444860320)

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Example text

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. This s u c t i o n gives r i s e t o a s t r e t c h i n g of the vortex l i n e s and hence an increase of the i n t e r i o r v o r t i c i t y (another very common example of t h i s process i s the s t r e t c h i n g of vortex l i n e s by g r a v i t y a s water drops down the d r a i n i n a bathtub: t h i s spins up the f l u i d i n t o a v o r t e x ) .

Set the cylinder on a uniformly r o t a t i n g t u r n t a b l e and allow enough time f o r t h e f l u i d t o achieve r i g i d body r o t a t i o n . Without d i s t u r b i n g the f l u i d , move the small b a l l slowly with v e l o c i t y 1 r e l a t i v e t o the r o t a t i n g f l u i d ( t h i s could possibly be done with a magnet if the b a l l were magnetized). physical parameters c),v,U,L such t h a t so t h a t the flow i s geostrophic. 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 .

We w i l l a l s o e x p l i c i t l y include g r a v i t y , w r i t i n g VG = -g1. 8) Geost rophic flow Co-ordinates i n a s p h e r i c a l s h e l l FIGURE 3 27 8-Plane approximation 28 Now i n oceanographic o r meteorological problem i t i s reasonable t o assume t h a t t h e f l u i d is constrained t o move i n a narrow s h e l l where $, << 1, [see Figure 31. << equation then implies t h a t can be neglected with respect t o i n the e q u a t o r i a l regions where The divergence 1.

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