The development of nonlinearities in the E to the 1/3 Stewartson layer

The present paper develops a formal asymptotic analysis for the growth of nonlinearities in the one-third Stewartson layer formed by the flow from a line source in a rotating fluid. When the Rossby number, epsilon, is large compared to E to the 1/2, for Ekman numbers E, it is found that inertial forces need be included in a domain with width O(epsilon to the 1/2 times E to the 1/4) and height O(epsilon to the 3/2 times E to the -1/4), which grows in size for increasing epsilon. Within this domain there are separate subdomains which can be recognized.