Turbulent Channel Flows on a Rotating Earth

Abstract

Abstract This paper deals with flow in a rectilinear channel on a rotating earth. The flow is directed perpendicular to the background planetary vorticity; both an analytical theory and numerical simulations are employed. The analytical approach assumes the existence of an eddy viscosity and employs a perturbation expansion in powers of the reciprocal of the Rossby number (Ro). At lowest order, a cross-channel circulation arises because of the tilting of the planetary vorticity vector by the shear in the along-channel direction. This circulation causes a surface convergence, which achieves its maximum value at a channel aspect ratio (= width/depth) of approximately 10. The location of the maximum surface convergence moves from near the center of the channel to a position very near the sidewalls as the aspect ratio increases from O(1) to O(100). To include the effects of turbulence, direct numerical pseudospectral simulations of the equations of motion are employed. While holding the friction Reynolds number fixed at 230.27, a series of simulations with increasing rotation (Ro = ∞, 10, 1.0, 0.1) are performed. The channelwide circulation cell observed in the analytical theory occurs for the finite Rossby number, but is displaced by lateral self-advection. In addition, turbulence-driven corner circulations appear, which make the along-channel maximum velocity appear at a subsurface location. The most interesting effect is the segregation of the turbulence to one side of the channel, while the turbulence is suppressed on the opposite side.