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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Additional info for An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics
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”). w induced a t t h e top and bottom I f t h e angular v e l o c i t y of both t h e t o p and t h e bottom is increased, t h e induced v e l o c i t y a t z and = 0 z = 1 w i l l be of opposite s i g n s ( r e c a l l t h e EKman layer analysis).
1) a) Problems Show t h a t the Rossby number measures the r a t i o of the convective force t o Coriolis force. b) Show t h a t t h e Ekman number measures the r a t i o of the viscous f o r c e t o Coriolis f o r c e . 2) Assume t h a t a c h a r a c t e r i s t i c surface s t r e s s of magnitude fluid. S generates motion i n a r o t a t i n g Introduce appropriate non-dimensional co-ordinates and determine the relevant nondimensional parameters. 2) = 0. Hence the momentum equation has reduced t o a balance between C o r i o l i s force and the pressure gradient.
23). 25), no longer and a c r u c i a l mechan- i s m by which v o r t i c i t y can be changed i n a r o t a t i n g f l u i d i s absent. Problems 54 Chapter 5 P r o b l e w Derive the f-rst order steady 3w i n a cy Lnd e r with the following boundary conditions. 3 9= C J -r8 at z=O +r^e at z=1 r5 at z=1. = = Legend has it t h a t the oceanographer Ekman was led t o i n v e s t i g a t e the viscous boundary l a y e r a t the surface of the ocean a f t e r observing an iceberg move a t r i g h t angles t o the w i n d .
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics by Susan Friedunder (Eds.)