In the first part of the study, we use two different analytical methods to compute the separation latitude's migration rate. The first method involves integrated balances and the second involves the path equation for the separated flow. Using the first approach, it is found analytically that the flow consists of one current intruding into the area occupied by the other. A fully developed intrusion (at $t rightarrow infty)$ is steadily propagating. Using the asymptotic expansion based on the scale analysis, we derive the formulae for the migration speed and the width of the steadily propagating intrusion. Using the second approach, the original initial value problem is reduced to a single time-dependent path equation for the separated current. It is shown analytically that, as should be the case, in the limit $t rightarrow infty$ the path equation solution is identical to the earlier solution for the steadily propagating intrusion.