SECT. 3] 



DYNAMICS OF OCEAN CURRENTS 



387 



for Rossby waves by inserting into (251) the values: Hi — SQO m, 7/ = 4000 m, 

 Aplp = 2x 10-3, g=lO^ cm sec-^ /= lO-i sec-i and /8 = 2x lO-i^ cm-i sec-i. 

 We obtain 200 m sec-i for cb and 3.6 m sec""i for Cg. The Rossby waves will 

 have periods in excess of Tmin., where 



Tmiu. = 27r/aJmax = 47r//j3c 



= 3.6 days for barotropic waves 

 = 6.8 months for baroclinic waves. 



The wave-lengths for zonal waves for the minimum periods are 



277/Ao = 4:7TOJmaxl^ = 27rc// 



= 12,600 km for barotropic waves 

 = 230 km for baroclinic waves. 



(253) 



(254) 



Fig. 5. Variation of wave number with angular velocity for zonal barotropic Rossby and 

 higher frequency waves. The curves are computed for c^/f^ = 0.2 and presented in 

 non-dimensional form with k'—fk/^ and cL>' = co/f. For comparison, the relationship 

 (broken curve) between k' and cv' is shown for uniform rotation {^ — 0) and for no 

 rotation (k= ±co/c). The curves are symmetrical with respect to the origin. 



The ratio of wave-length to period yields the phase velocity of the waves. For 

 the barotropic mode, the phase velocity is about 40 m sec-i and for the baro- 

 clinic mode, only 1.3 cm sec^i. The relation between wave number and angular 

 velocity for zonal waves is shown in non-dimensional form in Fig. 5. Curves 

 near 6u//= 1 are not shown because the approximations used in deriving (244) 

 are not valid in this region (eo -^ 00 for co — >/). 



The particle motion in Rossby waves is directed primarily along the crests 

 with a much weaker component in the direction of propagation. This may be 

 seen from (234) and (235) by forming the ratio \u\l\v\ ~ co//. The ratio is 

 about 0.2 for barotropic waves and about 4 x 10"^ for baroclinic waves at the 

 maximum angular velocity. The phase velocity a>/\/(A2 + v^) varies with the 

 direction of propagation of the waves. By substituting ko cos 6 for A and 



