Offset rotating plates in a uniformly rotating fluid

The flow identified by Berker (Encyclopedia of Physics, Springer, Berlin, 1963) on the motion induced between two parallel infinite plates rotating at angular velocity Omega with offset centers of rotation was solved by Abbot and Walters (J Fluid Mech 40:205-213, 1970). Here, we consider the same problem in a fluid uniformly rotating at angular velocity omega. The flow is then governed by a Reynolds number R and sigma = omega/Omega which represents the ratio of Coriolis to inertial forces. As in the original problem, the loci of centers of rotation projected onto the mid-plane form logarithmic spirals. Sample similarity profiles at fixed R and sigma are given in graphical form. Features of the logarithmic spirals in both the inertial and rotating frames of reference are also presented in graphical form.