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

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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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Extra resources for An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics

Example text

2) gives wo cI hence Q = 0, f; = 0. Thus t h e Ekman l a y e r equations a r e -ZG0 = 2Go = G Go uoc 5 + G OX Q5 o y + 9 13 = O . 12) combine t o give (5 14) The Elrman l a y e r since (Go lim 5-a + 16,) 41 = 0. o = n uo = Q1 = Q~ 90 so + E 1/’2 41 + at z=O, 5-0 at z=o, 5=0 ... 3. wo = 0 . and Also uo + uo, vo and wo = 0. a r e independent of z and t h e boundary conditions t h e r e f o r e imply n uo = Q1 Go = Q2 wo = 0 - Uo(X,Y) - V,(XJY) at 5=0 everywhere. 13), can be determined t o g i v e The Ekman l a y e r S u c t i o n c o n d i t i o n 42 Now wo = 0, hence t h e divergence e q u a t i o n i m p l i e s uox + v - 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”).

1) i n t h e EKman l a y e r where EV = + S u b s t i t u t i o n of t h e expan- O(E1’2). s i o n i n t o t h i s equation gives t o f i r s t order Now Po - O = - E - 1/2 0 as 5 - co Po Po hence . s = 0. 2) gives wo cI hence Q = 0, f; = 0. Thus t h e Ekman l a y e r equations a r e -ZG0 = 2Go = G Go uoc 5 + G OX Q5 o y + 9 13 = O . 12) combine t o give (5 14) The Elrman l a y e r since (Go lim 5-a + 16,) 41 = 0. o = n uo = Q1 = Q~ 90 so + E 1/’2 41 + at z=O, 5-0 at z=o, 5=0 ... 3. wo = 0 .

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