3. Prediction of Gulf Stream Meanders Using Harmonic Components 



Observations of the northern edge of the Gulf Stream show a system 

 of long waves which usually move toward the east. If these waves are 

 assumed to be similar to atmospheric waves, the Rossby wave theory asserts 

 that in an eastward flowing current the shorter waves should move the most 

 rapidly eastward, that longer waves should remain nearly stationary, and 

 that the longest waves will retrogress. Thus the wave system of the Gulf 

 Stream is treated as dispersive. 



The harmonic component prediction method is accomplished by first 

 digitizing the observed wave-like northern edge of the Gulf Stream relative 

 to the historical mean axis. The digitized curve is then resolved into 

 its first 10 harmonic components to find the amplitude of each harmonic. 

 Using a dispersive wave equation to find movement of each harmonic wave 

 through a prediction period, the predicted Gulf Stream position is deter- 

 mined by recombining the components. 



The Gulf Stream was digitized by measuring at equal intervals of 

 X (along the mean position) the normal distance (Y) to the observed 

 position of the Gulf Stream. In order to avoid unreal amplitude of the 

 first harmonic, the mean axis was adjusted by adding or subtracting a 

 constant to Y, so that area enclosed by the curve above the axis equals 

 the area below. 



After the Gulf Stream was digitized, the amplitudes (A,B) of each 

 harmonic component were determined by: 



^1 = 



z 



Y sin 



2iiix 



2 1 Zirix 

 ^i = _Z Y cos 



(11) 



where: 



L = total length of the Gulf Stream path along the mean axis of 

 flow (also length of first harmonic) 



N = total number of points along x-axis 



1 = harmonic number (1 = 1, 2, ..., 10) 



X = length along axis from origin 



Y = normal distance of the historical mean axis from observed track 



Next, the phase speed (Cj) of each harmonic wave was determined by the 

 dispersive Rossby wave equation: 



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