THE NUMERICAL PREDICTION OF MEANDERS IN THE GULF STREAM 



by 



James G, Welsh 

 The Travelers Research Center, Inc. 

 250 Constitution Plaza 

 Hartford, Connecticut O6IO3 



INTRODUCTION 



The equivalent barotropic model has enjoyed considerable predictive suc- 

 cess in meteorology. That this same model can be adapted to oceanographic 

 prediction is suggested by work of Warren (I963), in which he demonstrates 

 that the observed meanoer patterns in the Gulf Stream agree remarkably well 

 with constant potential-vorticity trajectories along the Continental Rise. 



The work described here is being carried out by The Travelers Research 

 Center, Inc., under contraci- to the U.S. Naval Oceanogr^hic Office. The pur- 

 pose of this work is to investigate the possibility for useful dvnamical pre- 

 diction of the Gulf Stream with an equivalent barotropic model especially 

 adapted for the ocean. 



DERIVATION OF THE EQUIVALENT BAROTROPIC MODEL FOR THE OCEAN 



When formulating hydrodynamic models, one must always impose certain con- 

 ditions and assun^)tions on the theoretical fluid in order to facilitate the 

 derivation of a practicail set of mathematical equations. The equivalent baro- 

 tropic model, as formulated f®r the ocean, is based upon these assumptions: 



The fluid is incompressible. 



The fluid is hcanogeneous . 



The fluid is inviscid. 



The fluid is in hydrostatic equilibrium. 



The direction of the flow is independent of depth except for the pos- 

 sibility of reversal, but the speed may have an arbitrary variation. 

 The last assumption contributes "equivalent" to the model's name, since both 

 speed and direction of a barotropic flow are independent of depth. It is 

 further assimied that: 



The fluid is bounded on top by a rigid, horizontal surface. 



The fluid is bounded below by a rigid bottom with variable slope. 



The flow is essentially horizontal and non-divergent and may there- 

 fore be defined by a stream function. 



As a point of departure for deriving the prediction equation appropriate 

 to the model, we start with the vorticity equation: 



1^ -^VV(3^f) i- (3^f)V'V= 0, (1) 



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