Turbulence-induced rectified flows in rotating fluids

Abstract

Laboratory experiments dealing with Reynolds stress gradients in shear-free turbulence inhomogeneous rotating fluids were conducted to better understand associated physicalphenomena. The study was motivated by possible applications to the oceanic environment wheresuch Reynolds stress gradients are ubiquitous (e.g. in the vicinity of the continental shelfbreak, where turbulence decays away from the boundary). The turbulence was generated byvertical oscillations of a circular shaft with O-ring surface roughness elements; the oscillation axis coincided with theaxis of symmetry of the cylindrical test cell.

In the absence of background rotation, the turbulence is strong in the immediate vicinityof the shaft surface and decays with the radial distance, r. The turbulencein the boundary layer is such that u_r∼u_θ∼w,where u_r, u_θ, w are the radial, azimuthal and vertical r.m.s. velocity components,respectively. These velocity components are found to be proportional to Sω,where S and ω are the stroke and frequency of the shaft oscillations,respectively, i.e. much the same as for the case of oscillating-grid turbulence, which hasbeen studied extensively.

When background rotation is present, the steady-state turbulent intensity close to theshaft is similar to that of the non-rotating experiments. Away from the shaft, in thecentral portion of the test cell, large-scale motions containing randomly distributedcyclonic and anticyclonic vortices are developed owing to small local Rossby numbers. In thevicinity of the shaft, a rectified anticyclonic flow U_θ isobserved. The magnitude of U_θ is found to be proportional to thecharacteristic r.m.s. turbulence velocity u, but independent of the rate ofbackground rotation.

Consideration of the equations of motion shows that mean flows should not be expected ifbackground rotation is absent. With rotation, however, the equations indicate that theturbulent stresses can initiate, further develop and then maintain a mean anticyclonic(rectified) flow around the cylinder; the azimuthal momentum equation is shown to play acritical role in the generation of the mean anticyclonic flow.