that from the innocuous initial condition, interesting and realistic features 

 vd.ll form in the diannel. 



RF.SULTS 



In practice, the model has developed features with wavelengths typically 

 on the order of i+OO km. Although some interesting features form, especially- 

 near the sea mounts extending southeastward from New England, the usefulness 

 of the jredictions is marred by an instaW-lity near the inflow. Tests to 

 study the effect of inflow profile and A* were conducted, but the occurrence 

 of the instability near the inflow may well obscure the true result of such 

 tests , 



The instabilitj'- is in the form of a single amplifying wave extending in 

 frcjn the inflov, with a wavelength of about 350 km. The amplification is such 

 that after typically 10 to 15 days, the prediction is completely unrealistic 

 near the inflow. The present effort is directed toward a theoretical under- 

 standing of the instability and toward devising the optimum means to control 

 it, since it does not seem to be an observed phenomenon of the Qulf Stream, 

 Two preliminary results of this investigation are discussed in the last two 

 sections of the paper, 



INFLCfbJ-OUTFLOW BALANCE 



The first modification to the model concerns the net transport of vorti- 

 city through the channel. It will be shown that a net accumulation or deple- 

 tion of relative vorticity will occia? in the channel unless the inflow and 

 outflow are selected to avoid it. Returning to equation (12), we may rewrite 

 it as: 



§-^V'Vio -§^V'{py), (20) 



where p = A «5 S- f - f ^ log h , and the divergence of V is neglected. Now, 

 by integrating equation (20) over the area R of the channel, 



/f§^da-^ff V'fpvm =0. (21 ) 



The left-hand integral in equation (21 ) represents the total acctmiulation or 

 depletion of relative vorticity in the channel. This should be zero for any 

 long-term prediction. The right-hand integral in equation (21 ) can be trans- 

 formed by Greene's theoresn into a line integral, 



Jjf V' (pV)JCL ^fp V'h ds = 6>, (22) 



for balanced inflow- out flow; \n is the outward-directed normal on the bound- 

 ary S of R , For the prediction channel, there is no cross-boundary flow 

 along the sides. At the inflow V«n = -v , and at the outflow V»n = v , 



143 



