These curves are conservative, i.e., they do not grow or change 

 downstream. The Gulf Stream has been observed to leave the Cape Hatteras 

 area with little tendency to meander; however, as the stream progresses 

 into the open ocean, meanders become larger and larger, indicating greater 

 angles of maximum deflection. A modification which allows the angle of 

 maximum deflection to increase linearly along the path is given by: 



= U + (Ap) S/D 



(3) 



where p' = the modified maximum angle, and Ay = the change of the maximum 

 angle of deflection along one wave. Because the wavelengths become shorter 

 as the angle of maximum deflection increases, an additional modification was 

 required; therefore AS, the distance between points, was also made to in- 

 crease linearly along the path. 



AS' = AS + [A(AS)] S/D 



(A) 



where AS' = modified distance between points anywhere along the curve and 

 A (AS) = the amplification factor which is the increase in the distance 

 between points along one wave. Equations (1) and (2) may now be rewritten 

 using these new modifications substituting p' for p and AS' for AS. 



Several examples of modified sine-generated curves are presented 

 in figure 2. In this figure, the change in angle of maximum deflection 

 and the distance increment amplification factor are indicated over the 

 entire path of the wave. In these examples, the curves are followed through 

 five waves . 



MAXIMUM ANGLE OF DEFLECTION = 0° TO 135° 

 AMPLIFICATION FACTOR = I 



MAXIMUM ANGLE OF DEFLECTION = 0" TO 135 = 

 AMPLIFICATION FACTOR = 5 



,tA/M 



MAXIMUM ANGLE OF DEFLECTION = 40° TO 180° 

 AMPLIFICATION FACTOR = 5 



Figure 2. Examples of Modified Sine-Generated Curves 



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