An experimental study of mean flow generation by Reynolds-stress gradients under rotational effects

Laboratory experiments have been conducted which demonstrate that a mean azimuthal flow can be produced by subjecting Reynolds-stress gradients to background rotation. It is thought that this mechanism may play a role in the generation of mean currents in coastal regions.; The experiments entail the establishment of boundary turbulence in a thin annular-shaped region centered within a cylindrical test cell through the use of a vertically oscillating grid. This region rests in a horizontal plane perpendicular to the vertical axis of the tank. The entire system is placed on a turntable to simulate the effects of background rotation. Flow visualization techniques are used to depict the qualitative features of the resulting flow field. Measurements of the mean and turbulent velocity fields are performed using a two-component laser-Doppler velocimetry system. The governing parameters include the temporal Rossby number, {dollar}Rosb{lcub}t{rcub},{dollar} the grid Reynolds number, {dollar}Resb{lcub}turb{rcub},{dollar} and various geometric ratios.; In the absence of rotational effects, the flow in the vicinity of the annulus is characterized by a mean-circulation in the (r,z) plane. The radial distribution of rms velocity {dollar}(usb{lcub}rms{rcub}){dollar} indicates tightly concentrated turbulence over the annulus region with a general form of {dollar}usb{lcub}rms{rcub}(r)sim esp{lcub}-rsp2{rcub}.{dollar} The term, {dollar}overline{lcub}usbsp{lcub}r{rcub}{lcub}prime{rcub}wspprime{rcub},{dollar} is the only nonzero Reynolds-stress component.; Under the effects of rotation, the Reynolds-stress term, {dollar}overline{lcub}usbsp{lcub}r{rcub}{lcub}prime{rcub}usbsp{lcub}theta{rcub}{lcub}prime{rcub}{rcub},{dollar} becomes nonzero. This produces counter-flowing mean azimuthal motions, with an anticylconic portion in the outer region of the annulus and a cyclonic portion in the inner region. These scale as the characteristic rms velocity of the turbulence. Consideration of the Reynolds-averaged mean momentum equations show that the initially unsteady mean flow develops through a balance of the horizontal Reynolds-stress gradient term, {dollar}overline{lcub}usbsp{lcub}r{rcub}{lcub}prime{rcub}usbsp{lcub}theta{rcub}{lcub}prime{rcub}{rcub},{dollar} and the mean azimuthal acceleration term, {dollar}partial Usb{lcub}theta{rcub}/partial t.{dollar} In this case, {dollar}overline{lcub}usbsp{lcub}theta{rcub}{lcub}prime{rcub}wspprime{rcub}{dollar} is also nonzero, while {dollar}overline{lcub}usbsp{lcub}r{rcub}{lcub}prime{rcub}wspprime{rcub}{dollar} becomes negligible. This indicates that the general flow structure is no longer confined to the (r, z) plane, but also those of the {dollar}(theta,z){dollar} and {dollar}(r,theta){dollar} planes.; Results presented include the mean, turbulent and Reynolds-stress distributions as a function of radius and height for a range of forcing frequency, {dollar}omega,{dollar} and rotation rate, f. Rotating and nonrotating cases are contrasted, and Reynolds-stress trends discussed with variations in the system parameters. Functional relationships are also developed at two selected measurement points over the annulus. These serve to link nondimensional input parameters, {dollar}Resb{lcub}g{rcub}{dollar} and {dollar}Rosb{lcub}t{rcub},{dollar} with measured output variables, such as normalized mean and rms velocities.