We consider initially isotropic homogeneous turbulence which is submitted to an external force, in statistically axisymmetric configurations. First, we study hydrodynamical turbulence in a rotating frame, in which case the Coriolis force modifies the structure and dynamics of the flow, thus creating elongated structures along the axis of rotation, corresponding to an accumulation of energy in the neighbourhood of the equatorial spectral plane. Secondly, a very similar configuration is that of magnetohydrodynamics (MHD) of a conducting fluid within an externally applied space uniform magnetic field, in which case the Lorentz force also concentrates energy to the same spectral equatorial manifold, but creates axially extending current sheets, along the magnetic field. We more specifically consider the quasi-static limit at small magnetic Reynolds number, in which the induction equation is analytically solved. We study the anisotropy of each turbulent flow using progressively refined statistics applied to results of direct numerical simulations, and we show that an accurate characterization of the flow structure requires advanced two-point statistics, which are available easily only in spectral space.

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