Energy spectrum of superfluid turbulence with no normal-fluid component

The energy of superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart law. It is shown that for k<2π/l the energy spectrum is very similar to the Kolmogorov's -5/3 law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and l is the average intervortex spacing. The vortex length distribution converges to a scaling property reflecting the self-similarity of the tangle