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 calculated the energy spectra of the 3D velocity field induced by dilute and dense vortex tangles respectively, whose dynamics is calculated by the Biot-Savart law. In the case of a dense tangle, the slope of the energy spectrum is changed at $k=2\pi/l$, where $l$ is the intervortex spacing. For $k>2\pi/l$, the energy spectrum has $k^{-1}$ behavior in the same manner as the dilute vortex tangle, while otherwise the slope of the energy spectrum deviates from $k^{-1}$ behavior. We compare the behavior for $k<2\pi/l$ with the Kolmogorov law.