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
Applying t h i s c o n d i t i o n t o t h e problem g i v e s Since t h e problem i s axisymmetric, we will assume t h a t t h e s o l u t i o n is a l s o axisymmetric, i . e . , A = 0. 21) and ( 5 . 2 2 ) are independent o f all z. ae Expressions z and hence hold f o r Equating t h e s e two e x p r e s s i o n s g i v e s The Ekman l a y e r therefore 45 v = r/Z. S u b s t i t u t i o n of t h i s value f o r v w1 = - i n t o ( 5 . 2 2 ) gives -1 2 - The divergence equation f o r axisymmetric geostrophic flow i s hence ru i s a constant, which w i l l be equal t o zero i f the s i d e walls a r e r i g i d .
Type 1 motions a r e successfully applied t o describe such problems as wave s t a b i l i t y , v e r t i c a l propagation of energy, and Gulf Stream meanders. Motions of type 2 have q u i t e d i f f e r e n t properties and a r e used t o analyze the very slow motions of the i n t e r i o r of t h e ocean. Problems 33 Dter 4 Problems I n the t e x t we discussed the two dimensional nature of strongly r o t a t i n g flow. We remarked t h a t a b a l l moving across a strongly r o t a t i n g flow could move i n a s t r a i g h t l i n e , but i n a weakly r o t a t i n g flow the b a l l would be d e f l e c t e d by r o t a t i o n .
What physical assump- t i o n s must be made i n order t h a t t h e s e equations can be used t o explain the phenomenon of a Taylor Column? k + Assume t h a t B f ) = 0. i s small and c o n s t r u c t a l i n e a r i z a - t i o n of t h i s e q u a t i o n t o g i v e -d9 at 2p + p g = o . CHAPTER 5 THE EKMAN LAYER I n t h e previous s e c t i o n we i n v e s t i g a t e d the fundamental s t a t e of a r o t a t i n g f l u i d , namely geostrophic balance. equations ( 4 . l ) and ( 4 . 2 ) , From i t i s immediately demonstrated t h a t t h e v e l o c i t y and pressure f i e l d s i n a geostrophic flow a r e independent of t h e v e r t i c a l co-ordinate, and t h a t t h e qH = 21-K x v P .
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)