SUMMARYA numerical simulation is performed to investigate the ow induced by a sphere moving along the axis of a rotating cylindrical container ÿlled with the viscous uid. Three-dimensional incompressible Navier-Stokes equations are solved using a ÿnite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor-Proudman theorem is valid for the viscous rotating ow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (Ro) of 1 and 0.02 and the Reynolds numbers (Re) of 200 and 500. When Ro = O(1), inertia waves are exhibited in the rotating ow past a sphere. The e ects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the ow structure are examined. When Ro 1, as predicted by the Taylor-Proudman theorem for inviscid ow, the so-called 'Taylor column' is also generated in the viscous uid ow after an evolutionary course of vortical ow structures. The initial evolution and ÿnal formation of the 'Taylor column' are exhibited. According to the present calculation, it has been veriÿed that major theoretical statement about the rotating ow of the inviscid uid may still approximately predict the rotating ow structure of the viscous uid in a certain regime of the Reynolds number.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.