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