An experimental investigation of MHD quasi-two-dimensional turbulent shear flows

Abstract

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 < k_i, where k_{[lscr ]} is the integral-length-scale wavenumber and k_i 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).