Table 43 



ROSSBY'S LONG-WAVE FORMULA 



131 



Rossby * has shown that in the case of sinusoidal perturbations on a zonal current in an ideal, 

 frictionless, homogeneous, and incompressible atmosphere in horizontal motion, the relation 

 between the velocity of the undisturbed zonal current U and the phase velocity of the perturbation 

 c is given by: 



0L a 



U -c — 



4tt 2 



where /3 is the rate at which the coriolis parameter increases northward (assumed to be constant 

 with latitude for a given zonal current) and L is the wave length of the perturbation. L is most 

 conveniently measured in terms of degrees of longitude at the latitude in question. 2 Similarly 

 the resulting /3L 2 /(47r 2 ) is measured in terms of degrees of longitude per 24 hours; a supple- 

 mental column also gives the result in meters per second. 



Wave length — degrees of longitude 



1 Rossby, C.-G., Journ. Mar. Res., vol. 2, pp. 38-55, 1939. 



3 The length of a degree of longitude at various latitudes is given in Table 163. 



SMITHSONIAN METEOROLOGICAL TABLES 



1%'A lo 



