The Effect of the Earth’s Rotation on Channel Flow

Abstract

The influence that the rotation of the earth has on laminar channel flow is investigated theoretically. The full nonlinear Navier-Stokes equations relative to a reference frame rotating with the earth are solved numerically for laminar flow in a rectangular channel whose axis is aligned east-west: the orientation which yields the most drastic effect. It is demonstrated that for channels of moderate width (less than 1 ft for the flow of most liquids), the rotation of the earth can give rise to a roll instability which has a severe distortional effect on the classical parabolic velocity profile. Consequently, the usual assumption made of neglecting the effect of the earth’s rotation in the calculation of channel flow can lead to serious errors unless the channel is substantially smaller than this size. It is briefly shown that similar effects would be expected for turbulent channel flow when the channel width is approximately an order of magnitude larger.