392 FOFONOFF [sect. 3 



the waves along at the velocity, Uq. Consequently, we can apply the time- 

 dependent solutions already examined by replacing oj everywhere by co + Uok. 

 It is of particular interest to examine those solutions that are brought to rest 

 (a> = 0), relative to the boundaries, by the zonal flow. As Rossby waves move 

 westwards, they can be made stationary by an eastward flow. Replacing co by 

 Uok in (249) and simplifying the resultant equation, we obtain 



k^ + v^^^lUo, (277) 



where we have neglected terms of the order of /^/c^^ 10~i^ cm~2 and smaller 

 in comparison with /S/t/o~ 10"^"^ cm~2. Equation (277) is equivalent to the 

 characteristic equation for the homogeneous solutions of the vorticity equation 

 (101). Hence, the solution (104) consists of a steady zonal flow towards the east 

 with barotropic Rossby waves progressing westwards relative to the water, but 

 of such wave-lengths that the motion relative to the boundaries is zero. As 

 indicated by (256), Rossby waves of a given wave-length have the same west- 

 ward component of phase velocity so that they can be made stationary by a 

 uniform eastward flow regardless of their direction of propagation. The inertial 

 solution (104) includes a system of zonal currents that can be interpreted as a 

 stationary meridionally-directed Rossby wave. Only the short Rossby waves 

 appear in the inertial solution because the long waves have phase velocities 

 much larger than Uq and cannot be brought to rest by the zonal flow. 



For C7o<0, the aperiodic solutions given by (276) can be made stationary. 

 Substitution of Uok for oj in (276) yields 



A;2 = (^/|t/o|) + v2, (278) 



which is equivalent to the characteristic equation for the solution given in 

 (103). Hence, the inertial boundary currents along the western and eastern 

 boundaries can be considered as a time-dependent motion that propagates 

 eastwards at the same speed as the westward interior flow. Because of its 

 eastward motion relative to the interior flow, the western-boundary current 

 cannot be formed if the interior flow is eastward or zero. It is possible that, if 

 the westward interior flow weakens, the western-boundary current could not 

 adjust in time to prevent its breaking away from the boundary. If this were the 

 case, it would perhaps not be unreasonable to suggest that variations of the in- 

 terior flow could lead to breaking away and re-formation of the western- 

 boundary current yielding a "multiple-stream" structure such as that suggested 

 by Fuglister (1951). This result does not follow from the analysis presented 

 here although its possibility is suggested. Further investigation of the stability 

 of the western-boundary currents could yield significant results that would 

 improve our understanding of ocean circulation. 



The interpretation in terms of barotropic wave motion of the solutions for 

 inertial circulation in a homogeneous ocean cannot be extended to inertial 

 baroclinic circulation. The baroclinic Rossby waves move very slowly. Their 

 maximum westward phase velocity is of the order of 3 cm sec~i. As steady 

 velocities in the upper layers of the oceans are of the same magnitude or 



