Meanders 127 



blowing over water and introduced capillarity as an additional stabilizing 

 influence, which acts mostly on very short waves. As a result, the system is 

 stable for all wavelengths of perturbation if the wind is below a certain 

 critical speed. With increasing wind speed a single wavelength becomes 

 unstable. Kelvin proposed to apply this theory to the formation of wind 

 waves, but observation shows that real wind waves are more comphcated 

 than those envisaged in this simple theory. Even this problem, which at 

 first seems so easy and for which there is no lack of observational material, 

 has never been successfully resolved. 



Meteorologists must deal with problems of a vastly more complicated 

 nature when they attempt to apply the perturbation method to such 

 phenomena as the development of waves and cyclones in the atmosphere. 

 After J. Bjerknes and his co-workers discovered atmospheric fronts in 1919, 

 they came to regard cyclones as unstable waves of the common boundary 

 (incUned frontal surface) between two air masses with uniform (but different) 

 densities and velocities. Tentative approximate solutions were given by 

 V. Bjerknes, J. Bjerknes, Solberg, and Bergeron (1933). Owing to the fact 

 that there are two stabilizing factors — gravity, operating now on short 

 waves, and the earth's rotation, acting on the longest waves — the system is 

 dynamically stable so long as the wind shear is less than a critical value, but 

 when this value is just exceeded, a dominant unstable wave appears. This 

 was interpreted as a cyclone. 



The chief difficulty of this model is that it was soon discovered that 

 fronts never exist outside of cyclones, a fact which made it seem unlikely 

 that they could be the origin of cyclones. Some cyclones have no fronts 

 associated with them at all. With the increase of meteorological data it has 

 become increasing clear that cyclones are not the result of a degenerating 

 mean zonal motion; indeed, Starr (1953) suggests that they are the cause of 

 the mean motion. 



Modern meteorologists have abandoned the notion that large-scale 

 atmospheric perturbations are necessarily associated with discontinuities 

 (fronts), and have turned to other models, such as that of Rossby's (1947) 

 theory of long waves in the westerlies. Other present-day models involve 

 vertical wind shears, and horizontal temperature gradients (see Fjortoft, 

 1951, for a summary) of a form so remote from the structure of the Gulf 

 Stream that they are not likely to be of help in understanding meanders. 



When we come to consider the Gulf Stream, we are not embarrassed by 

 the difficulty involved in early cyclone theory : there is no doubt that the 

 Gulf Stream is the primary phenomenon, and that the meanders are 

 secondary. Hence the Gulf Stream may surely be regarded as the basic 

 undisturbed current, on top of which the meanders appear as perturba- 

 tions. 



