  We analyse the anisotropy of homogeneous turbulence in an electrically
conducting fluid submitted to a uniform magnetic field, for low magnetic
Reynolds number, in the quasi- static approximation. We interpret disagreeing
previous predictions between linearized theory and simulations: in the linear
limit, the kinetic energy of transverse velocity components, normal to the
magnetic field, decays faster than the kinetic energy of the axial component,
along the magnetic field (Moffatt (1967)); whereas many numerical studies
predict a final state characterised by dominant energy of transverse velocity
components. We investigate the corresponding nonlinear phenomenon using Direct
Numerical Simulations of freely-decaying turbulence, and a two-point
statistical spectral closure based on the Eddy Damped Quasi-Normal Markovian
model. The transition from the three-dimensional turbulent flow to a
"two-and-a-half-dimensional" flow (Montgomery & Turner (1982)) is a result of
the combined effects of short-time linear Joule dissipation and longer time
nonlinear creation of polarisation anisotropy. It is this combination of linear
and nonlinear effects which explains the disagreement between predictions from
linearized theory and results from numerical simulations. The transition is
characterized by the elongation of turbulent structures along the applied
magnetic field, and by the strong anisotropy of directional two-point
correlation spectra, in agreement with experimental evidence. Inertial
equatorial transfers in both DNS and the model are presented to describe in
detail the most important equilibrium dynamics. Spectral scalings are
maintained in high Reynolds number turbulence attainable only with the EDQNM
model, which also provides simplified modelling of the asymptotic state of
quasi-static MHD turbulence.
