Energy Spectrum of Vortex Tangle

The energy spectrum of superfluid turbulence in the absence of the normal fluid is studied numerically. In order to discuss the statistical properties, we calculate the energy spectra of the 3D velocity field induced by both dilute and dense vortex tangles, whose dynamics are calculated by the full nonlocal Biot-Savart law. In the case of a dense tangle, the slope of the energy spectrum changes at k=2(pi)/l, where l is the intervortex spacing. For k>2(pi)/l, the energy spectrum has a k-1 behavior in the same manner as the dilute vortex tangle, while otherwise the slope of the energy spectrum deviates from the k-1 behavior. We compare the behavior for k<2(pi)/l with the Kolmogorov law.