A. INTRODUCTION 



During the past four years, the U. S. Naval Oceanographic Office has 

 been conducting airborne oceanographic research surveys of the western 

 North Atlantic Ocean including mapping the position of the Gulf Stream's 

 northern edge. As these data became available, statistical studies were 

 made of certain characteristics of the Gulf Stream, such as its mean path, 

 speed of its meanders, and the limits of its northern edge. At the same 

 time, attention was turned to applying and testing methods for predicting 

 the Gulf Stream's northern edge. 



This paper describes four numerical simulation methods for predicting 

 the Gulf Stream's northern edge as follows: (1) application of river 

 meander theory to Gulf Stream meanders, (2) the relation of the Gulf 

 Stream to paths of constant potential vorticity, (3) movement of harmonic 

 components of Gulf Stream meanders using a dispersive wave equation, and 

 (4) a simple dynamic model of the Gulf Stream by numerical Integration 

 of the vorticity equation. Brief descriptions of these methods have 

 appeared in the Gulf Stream Summary (6, 7, 8, 9, 10). 



B. MATHEMATICAL SIMULATION METHODS 



1. Application of River Meander Theory to Gulf Stream Meanders 



Leopold and Langbein (2) described a mechanism for river meanders 

 which appeared to be feasible as a mechanism for generating Gulf Stream 

 meanders. River meanders can be simulated by curves that require a 

 minimum of work in turning. Such curves have maximum radii of curvature 

 and can be derived by minimizing the integral of energy required to alter 

 the direction of the river. These curves can be closely approximated by 

 sine-generated curves, i.e., the tangential direction of the resulting 

 curves varies sinusoidally . 



Figure 1(a) shows an example of a sine-generated curve, and 

 figure 1(b) shows the direction plotted as a function of distance down- 

 stream. Angles are measured from the direction of the mean path, posi- 

 tive to the left and negative to the right. Since the tangential 

 direction varies sinusoidally, 



a = y cos ±ZL§. (1) 



D 



where: 



a = tangential direction of curve at some point along curve 



y = maximum angle of deflection [e.g., at points 1, 3, 5, 

 and 7 in figure 1(a), where a = 90"] 



S = distance measured along curve from the starting point 



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