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 thought of geophysical fluid dynamics (NH Pub. Co., 1980)(ISBN 0444860320)

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Hence, a s we would expect from t h i s system of equations where each term i s 0(1), the time dependence decays t o give a steady s o l u t i o n on a time s c a l e of O ( 1 ) . I n other words, the steady Ekman layer has developed a t t h e boundary a f t e r a couple of revolutions. 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 .

Eo ‘L cos -z eo[e-e,l sin + .... 14) az We have therefore approximated the problem of flow i n an ocean basin by flow on a plane r o t a t i n g about an axis ponding t o ^r a t point (610,$o)), with A kt an angular v e l o c i t y which i s no longer constant, but v a r i e s l i n e a r l y with [Note increasing on the plane]. y (corresy. 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.

8) v cos 8 cos 8 everywhere -, 0. The narrow s h e l l assumption a l s o enables us t o approximate radius % of the sphere. 9), = -g. 11) a r e the geostrophic approxima- t i o n f o r a spherical s h e l l . The equations f o r geostrophic balance i n a s p h e r i c a l s h e l l a r e of course s i m i l a r t o the Cartesian equations ( 4 . 4 ) . " Consider an ocean, o r s e c t i o n of the atmosphere centered a t a c o - l a t i t u d e 8*: we then assume t h a t the l a t i t u d i n a l s c a l e of the problem is small enough t h a t we can neglect the curvature of the e a r t h and approximate the Geos t rophic flow geometry by a tangent plane centered a t E The tangent plane FIGURE 4 29 8,.

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