130 Meanders 



waves. These are of most interest to us because they are the only ones 

 likely to grow large enough to be noticed on a ship survey. Examination of 

 the coefficients of the frequency equation reveals that for U^ < g'D all waves 

 are stable. At U^ = g'D a single wave number given by k=fj^'2 U becomes 

 'just unstable', whereas all other wave numbers are stable. For shghtly 

 larger values of U'^ there is a narrow range of wave numbers about k =fj^j2 U 

 in which waves are unstable. In the critical case of margmal stabUity the 

 'just unstable' wave is stationary. 



One objection to appljang this model to the meanders observed in the 

 Gulf Stream is that the real Gulf Stream is not very wide. A more sophisti- 

 cated theory would include lateral boundaries to the Stream and would 

 provide for resting layers of water on each flank beyond the boundaries. 

 Also, a perturbation theory appHes only to waves of infinitesimal amplitude, 

 whereas meanders often grow to large ampHtude. Therefore it is important 

 to regard this treatment of meanders as merelj^ indicative of a possible 

 mechanism for describing the meandering of a stratified current; but it is 

 hard to see how it could be tested by actual observation of the crests and 

 troughs of meanders, because the theory and observational techniques are 

 both too crude to admit of a meaningful comparison. 



Application to the Gulf Stream. — Rossby (1951) has shown that the 

 velocity of the Gulf Stream does in fact approach the critical value ^!{g'D). 

 This is also true for the stream of uniform potential vorticity (see Chapter 

 VIII). We might expect the Stream to become progressively shallower 

 downstream as a result of friction, and gradually to approach the critical 

 condition. Because of the paucity of hydrographic sections of the Stream 

 in any one year or season, it is necessary to construct a composite series of 

 sections, in order to determine whether there is any noticeable change in 

 the depth of the Stream along its axis. A number of sections aU made in 

 early June of several years have been assembled and recomputed: (i) one at 

 Hatteras at about 74° W. ; (ii) two more on the Montauk Point-Bermuda 

 line surveyed in IseUn's (1940) studies; (iii) one at 58° W.; and (iv) two Ice 

 Patrol sections along the 50° W. meridian. The geostrophic transports at 

 different depths were computed. In order to exhibit any changes in the 

 depth of the Stream, the percentage of the total transport below certain 

 selected depths was computed. The results are given in table 6; it is clear 

 that there is no striking change in the depth of the Stream indicated by 

 these sections. The inference to be drawn from this is that from Cape 

 Hatteras to the tail of the Grand Banks the Stream is near to the critical 

 velocity almost everywhere, and that unstable meanders might be expected 

 anywhere. 



We may ask ourselves what the size of the meanders predicted by our 

 two-layer meander theory might be expected to be. A surface layer 200 m. 



