Laboratory experiments dealing with Reynolds stress gradients in shear-free turbulence in
homogeneous rotating fluids were conducted to better understand associated physical
phenomena. The study was motivated by possible applications to the oceanic environment where
such Reynolds stress gradients are ubiquitous (e.g. in the vicinity of the continental shelf
break, where turbulence decays away from the boundary). The turbulence was generated by
vertical oscillations of a circular shaft with O-ring surface roughness elements; the oscillation axis coincided with the
axis of symmetry of the cylindrical test cell.
In the absence of background rotation, the turbulence is strong in the immediate vicinity
of the shaft surface and decays with the radial distance, r. The turbulence
in the boundary layer is such that
ur∼uθ∼w,
where ur, uθ,
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 has
been studied extensively.
When background rotation is present, the steady-state turbulent intensity close to the
shaft is similar to that of the non-rotating experiments. Away from the shaft, in the
central portion of the test cell, large-scale motions containing randomly distributed
cyclonic and anticyclonic vortices are developed owing to small local Rossby numbers. In the
vicinity of the shaft, a rectified anticyclonic flow Uθ is
observed. The magnitude of Uθ is found to be proportional to the
characteristic r.m.s. turbulence velocity u, but independent of the rate of
background rotation.
Consideration of the equations of motion shows that mean flows should not be expected if
background rotation is absent. With rotation, however, the equations indicate that the
turbulent stresses can initiate, further develop and then maintain a mean anticyclonic
(rectified) flow around the cylinder; the azimuthal momentum equation is shown to play a
critical role in the generation of the mean anticyclonic flow.