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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Extra resources for An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics
N terms of t h e dimensionless para- meters, and in t h e r o t a t i n g c o - o r d i n a t e system, t h e boundary conditions a r e We write 9 4 = 9 = re^ a t 0 at Z=O z=1. i n c y l i n d r i c a l co-ordinates 9 = u; + ve" (r,e,z) as + wi;. 20) a t z=O gives To analyze t h e EKman l a y e r a t and a az - -E- ''' a t . gE1/2 Hence we o b t a i n a s i m i l a r e x p r e s s i o n f o r t h e s u c t i o n c o n d i t i o n , but with a s i g n change, namely where € & is t h e imposed v e l o c i t y of t h e t o p s u r f a c e .
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 . Illustrate t h i s statement by considering t h e following mathematical problem. Consider a Taylor Column bounded between h o r i z o n t a l p l a t e s a t z = 0 and Neglect t h e e f f e c t s of boundaries i n the y z = 1.
2 0 ) which was d e r i v e d a s a boundary c o n d i t i o n h o l d i n g a t f o r a l l v a l u e s of and z=O, must i n f a c t hold z, s i n c e t h e q u a n t i t i e s involved, wl, go €&, a r e a l l independent of z. We w i l l g i v e a n example t o i l l u s t r a t e t h e power of t h i s r e s u l t i n d e t e r m i n i n g t h e s t e a d y flow i n a r o t a t i n g c y l i n d e r . n terms of t h e dimensionless para- meters, and in t h e r o t a t i n g c o - o r d i n a t e system, t h e boundary conditions a r e We write 9 4 = 9 = re^ a t 0 at Z=O z=1.
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)