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 $k<2\pi /l$ 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.

• Received 22 January 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.145301