Decay of a quantized vortex tangle at a very low temperature

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We studied theoretically and numerically the vortex dynamics in superfluid helium and Bose-Einsteincondensate of Alkali atomic gas. The obtained results are the following.Superfluid helium : We studied the energy spectrum of superfluid turbulent state, thus finding the Kolmogorov -5/3 law which is the most important statistical law in classical turbulence. The diffusion of a vortex tangle is studied. The vortex tangle under rotation was found to be polarized along the rotational axis.Alkali atomic Bose-Einstein condensate : By studying numerically the Gross-Pitaevskii equation under rotation, we found that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice; the results are qualitatively consistent with the experimental results.