An extensive experimental study is carried out to examine the properties of a
quasi-two-dimensional MHD turbulent shear flow. Axisymmetric shear of a mercury layer
is enforced by the action of a steady vertical magnetic field and a radial horizontal
electric current flowing between a ring set of electrodes and a cylindrical wall. This
shear layer is unstable, and the properties of the turbulent flow are studied for a wide
range of Hartmann (up to 1800) and Reynolds numbers (up to 106). The mean velocity
profiles exhibit a turbulent free shear layer, of thickness larger than that predicted
by the laminar theory by two orders of magnitude. The profiles yield the expected
linear dependence between the total angular momentum and the electric current
when the magnetic field is large enough, but demonstrate a systematic deviation when
it is moderate (Ha [lsim ] 250). The quasi-two-dimensional turbulence is characterized
by an energy transfer towards the large scales, which leads to a relatively small
number of large coherent structures. The properties of these structures result from
the competition between the energy transfer and the Joule dissipation within the
Hartmann layers. In the intermediate range of wavenumbers
(k[lscr ] < k < ki, where
k[lscr ] is the integral-length-scale wavenumber and ki
the injection wavenumber), the energy spectra exhibit a power law close to
k−5/3 when the Joule dissipation is weak and
close to k−3 when it is significant. The properties of the turbulent flow in this latter
regime depend on only one non-dimensional parameter, the ratio
(Ha/Re)(l⊥/h)2 (Ha
is the Hartmann number, Re the Reynolds number based on the cell radius, l⊥ a
typical transverse scale, and h the layer width).
Effects of the extensional rheological properties of polymer solutions on vortex shedding and turbulence characteristics in a two-dimensional turbulent flow