The motion induced by a radially stretching membrane in a rotating fluid system

The flowinduced above an impermeable sheet undergoing linear radial stretching in a system rotating at angular velocity Omega is investigated. The problem is governed by the single parameter sigma = Omega/a, where a is the stretching rate of the membrane. A similarity reduction of the Navier-Stokes equations leads to a pair of nonlinearly-coupled ordinary differential equations which are numerically solved over the range 0 <= sigma <= 10. Coriolis forces acting on the radially stretching flow in the vicinity of the wall induces azimuthal flow in the boundary layer. A large-sigma analysis of the system leads to the Ekman equations describing the balance of Coriolis and viscous forces for which an exact solution is presented. Numerical results for the radial and azimuthal shear stresses, along with the magnitude of the velocity induced into the boundary layer, are shown to be in good agreement with the large-sigma asymptotic results. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim