Document Type



This item is available under a Creative Commons License for non-commercial use only


Applied mathematics, Fluids and plasma physics, Applied mechanics

Publication Details

Physics of Fluids, 2001, Volume 13, Issue 8 .pp. 2279-2286. doi:10.1063/1.1384470 Available from


The flow generated in a viscous liquid contained in a cylindrical geometry by a rotating end wall is considered. Recent numerical and experimental work has established several distinct phases of the motion when fluid inertia plays a significant role. The current paper, however, establishes the nature of the flow in the thus far neglected low Reynolds number regime. Explicitly, by employing biorthogonality relations appropriate to the current geometry, it is shown that a sequence of exponentially decaying eddies extends outward from the rotating end wall. The cellular structure is a manifestation of the dominance of complex eigensolutions to the homogeneous problem and arises as the result of nonlinear forcing associated with an inertial correction to the Stokes flow.