Ci = U - -SliL (12) 



where: 



6 = change of Corlolis parameter to the north 

 U = velocity of the mean flow (30 cm/sec) 



Since the amplitudes of the sine and cosine components of each 

 harmonic and the phase speed of each harmonic are known, the position of 

 the northern edge of the Gulf Stream can be predicted at some time (t) 

 by: 



- 1« 2wi 

 Y = Y + X A. sin (x - c.t) 



i=l L 



10 

 + Z B cos ill (x - c,t) (13) 



i=l L ^ 



An example of an harmonic prediction of the Gulf Stream compared 

 to its measured position is shown in figure 6. The position of the 

 northern edge of the Gulf Stream was established during two flights on 

 11 and 12 April 1966. The prediction was made for 8.5 days later on 20 

 April, for which observed data are also plotted. Because this method 

 conserves energy in each component, development of large loops and eddies 

 is not possible. 



4, Prediction of Gulf Stream Meanders by Dynamic Two-Dimensional 

 Advection 



The above methods are essentially one-dimensional, with the Gulf 

 Stream represented by a line. The general features and circulation of a 

 region as well as positions of specific features are also of interest. A 

 two-dimensional ocean model similar to the model used in the second method 

 was used for Gulf Stream prediction. The ocean is homogeneous, frictionless, 

 and barotropic, with the added restraints of a horizontal bottom and top 

 and bounds of 33''N, 42''N, 65''W, and Tg'W. The area is subdivided into a 

 20-km grid. The vertically integrated vorticity equation is given by: 



d 

 _ (^+f) = (14) 



dt 



This is the equation for conservation of absolute vorticity. The vorticity 

 equation (14) is rewritten as: 



3C ^ -^ 



_ = - V • V (^+f) (15) 



3t 



-10- 



