Table 1 lists values of ^5 for several tjrpical values of A^ U and V , 

 Since the basic current is essentially westerly, features vfith wavelengths 

 longer than As for a given A* U and V will have easterly phase velocities 

 (i.e. , they retrogress) and features with wavelengths shorter than Ag will 

 have westerly phase velocities less than A* U , 



TH>: VERTICAL PROFILE OF THE CURRENT 



The parameter A' in the model equations (12) or (13) is a measure of 

 the vertical variability of the current. It should be evaluated fix)m obser- 

 vations of the current profile extending all the way from the surface to the 

 bottcm. Unfortunately, adenuate observations do not exist. Many current 

 profiles in the Gulf Stream extend only a few hundred meters below the sur- 

 face; also they assume a level of no motion near 200 meters. Direct measure- 

 ments of the current are almost entirely restricted to the surface of the 

 ocean. At depth, direct observations are simply too sparse to allow a real- 

 istic evaluation of A* . 



If A* cannot be evaluated, its behavior can be studied from hypotheti- 

 cal current profiles. Table 2 summarizes such a calculation. The surface 

 current speed is given as Vq , and the current at the bottom, 5000 meters, 

 is assumed to be 1/10 Vq , The current is constant from the bottom to some 

 intermediate depth d , and varies linearly from d to the surface, Frcan 

 Table 2 and similar profiles, it is observed that a reasonable range for 

 A* is 1,0 to 2.5. 



APPLICATION OF THE MODEL 



To apply the model, an array of grid points is _laid over a portion of 

 the Gulf Stream and the change of stream function Y' at the grid points 

 from some initial condition is computed by equation (12). 



Tne prediction area (Fig. 1 ) that has been used is in the form of a 

 channel containing the Gulf Stream from Cape Hatteras to the Grand Bank, 

 The inflow to the channel extends across the Gulf Stream for about 800 km in 

 a southeasterly direction from Cape Hatteras. The outflow from the channel 

 lies approximately along 50*^, One side of the channel lies along an arbi- 

 trary isobath of the Continental Shelf. The deep side of the channel follows 

 a broad arc passing west and north of Bermuda and about 700 kra from the edge 

 of the Continental Shelf. 



The grid points laid over the Gulf Stream are rectilinear on a polar 

 stereographic map projection and are 50 km apart. A computer program (IBM 

 7090) has been written to accept as initial conditions a bottcan topography at 

 all grid points and a stream-function profile along the inflow. The program 

 D:enerates an innocuous field of stream function at all grid points from the 

 specified inflow. The outflow stream-function profile is linear and no flow 

 is allowed across the sides of the channel. From this initial condition, the 

 model is numerically integrated in time steps of about one hour. It is hoped 



139 



