Superfluid turbulence has many interesting features which are the object of much current experimental and theoretical research. One of the recent aims of the research is to understand the coupling between turbulence and rotation, namely, to explore turbulence in the simultaneous presence of heat flux and rotation. Another current active topic of exploration is the influence of the walls on the features of turbulence. These two topics have been the object of our recent joint research. The analysis is based on dynamical equations for the superfluid vortex tangle, including the effects of the walls, of the heat flux and of rotation. The macroscopic effects of the vortices are described by means of a tensor, whose evolution equation must be determined; we study thermodynamic restrictions to such evolution equation, and we explore the tangle anisotropy, the influence of nonlocal terms, and intermittent aspects. Furthermore, we deal with the formation and the decay of vortices after sudden acceleration of the fluid. This analysis is expected to contribute, too, to the understanding of some aspects of classical turbulence related, in some suitable limits, to the behaviour of quantum turbulence.Amongst the possible applications, we study the flow of superfluids along thin capillaries in the presence of heat exchange with the surroundings, which is of interest for the refrigeration of small electronic circuits in supercomputers. In such an analysis, the coupling of hydrodynamic flow and heat flux is necessary to understand the working conditions optimizing heat exchange and minimizing turbulence.
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