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تسجيل مستخدم جديدEnergy Spectra of Developed Turbulencein Helium Superfluids
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We suggest a minimal model for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier-Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to the temperature dependent parameter $q=alpha/(1+alpha)$, where $alpha$ and $alpha$ denote the dimensionless parameters characterizing the mutual friction between quantized vortices and the normal component of the liquid. We then derive the energy balance equations, taking into account the cross-velocity correlations. We obtain all asymptotical solutions for normal and superfluid energy spectra for limiting cases of small/big normal to superfluid density ratio and coupling. We discuss the applicability limits of our model to superfluid He II and to $^3$He-B and compare the model predictions with available experimental data.
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