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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Additional info for An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics
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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