By Susan Friedunder (Eds.)
Friedlander S. An advent to the mathematical concept 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
Show t h a t the v e l o c i t y of the f l u i d i n the Taylor Column moving i n a s t r a i g h t l i n e s a t i s f i e s the l i n e a r geostrophic equations. Determine a n O(E) c o r r e c t i o n term t o the v e l o c i t y t h a t s a t i s f i e s an Oseen approximation t o t h e nonl i n e a r momentum equation. Consides the f u l l Navier-StoKes equations f o r the motions of a r o t a t i n g f l u i d . 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?
Corresponds t o the northward d i r e c t i o n I n l a t e r chapters we w i l l discuss i n d e t a i l the very i n t e r e s t i n g e f f e c t t h a t t h i s l a t i t u d i n a l v a r i a t i o n has on the behavior of a r o t a t i n g f l u i d , and show how i t can be used t o explain observed oceanographic phenomena. 14) again imply t h a t u v and a r e independent of v e r t i c a l co-ordinate . z , where z i s now the l o c a l However, combining t h i s system with the divergence equation, V'J = 0, implies Thus hf 3Y i s no longer zero Because conclude t h a t w e do a z = 0.
The steady Exman l a y e r w i l l now modify t h e i n t e r i o r v e l o c i t y by means of the c i r c u l a t i o n induced by E K M n layer suction. 49 The Ekman l a y e r This process i s known a s spin-up ( o r spin-down i f t h e boundary v e l o c i t y i s decreased r e l a t i v e t o n), and t h e time taken f o r the i n t e r i o r v e l o c i t y t o reach a new steady s t a t e i s c a l l e d t h e spin-up time s c a l e . 3 Thus = 0. V Now the v e r t i c a l v e l o c i t y boundaries is 0(E1”).
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)