An attempt to fit an amplifying sine-generated curve to an observed 

 Gulf Stream path Is shown in figure 3. The Gulf Stream, however, does not 

 behave as a river and the application of the river meander theory to Gulf 

 Stream meanders was not satisfactory. The fact that modifications of the 

 pure sine-generated curves were necessary indicates that the interaction of 

 dynamic forces of the Gulf Stream system are not adequately satisfied by 

 simply minimizing the work required in turning. 



SINE-GENERATED WAVE 



Figure 3. A Modified Sine-Generated Curve Compared to the Gulf Stream 



2. Relating Gulf Stream Meanders to Paths of Constant Potential 

 Vortlcity 



Warren (11) demonstrated that meanders of the Gulf Stream appear 

 to conserve potential vortlcity. That is, the flow of the Gulf Stream 

 responds primarily to changes in bottom topography and to a lesser ex- 

 tent latitude. Using this hypothesis, a model is described for use in 

 calculating the path of a hypothetical parcel of water as it leaves the 

 Cape Hatteras region. 



The equation for the conservation of potential vortlcity is 

 derived from the equations of motion by cross-differentiation and by 

 Imposing the condition of nondivergence. The ocean is assumed to be in- 

 compressible, homogeneous, frictionless, and barotropic under steady 

 state conditions with a constant velocity along the axis of the Gulf 

 Stream. The barotropic assumption requires current velocity to be con- 

 stant with depth. The restriction on current velocity differs from that 

 Imposed by Warren in that his model merely required that the current 

 extend to bottom without change of direction. 



The equation for the conservation of potential vortlcity can be 



written: 



= 



(5) 



where: 



? = relative vortlcity 

 f = Corlolls parameter 

 h = ocean depth 



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