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.