Study of the anisotropy in turbulent superfluids

In this review we are interested on the anisotropy and polarity of superfluid turbulence in helium II, a still open problem which needs more details. Though some of the results presented here have already been published in different papers, this short review aims to put the main results together and to extend them when necessary. From the mesoscopic viewpoint, an evolution equation for the vortex line density was proposed in rotating counterflow (heat flux without mass flux) by means of dimensional analysis. Then, starting from the microscopic viewpoint this evolution equation was further extended to include situations where turbulence is not homogeneously distributed. Indeed, microscopically a vortex is a line, so the distribution of vortices is characterized by tensors, for the anisotropy, and by vector for the polarity. These ingredients play a relevant role in the evolution equations fo the vortex line density, as well as in the dynamical equations for the normal and superfluid velocity, and they influence the hydrodynamic behaviour of superfluids flowing along tubes or in fastly rotating systems, as neutron stars.