Energy spectrum of grid-generated He II turbulence

A grid of bars towed through a sample of He II produces both superfluid turbulence and classical hydrodynamic turbulence. The two velocity fields—in the normal fluid and in the superfluid—have been observed to have the same energy spectral density over a large range of scales. Here, we introduce a characteristic scale [formula presented] where [formula presented] is the rate of turbulent energy dissipation per unit volume, and note that the energy spectrum in superfluid turbulence depends also on the quantum of circulation [formula presented] for wave numbers [formula presented] We propose that the spectral density in this range is of the form [formula presented] where C is the three-dimensional Kolmogorov constant in classical turbulence. This form is consistent with recent experiments in the temperature range [formula presented] on the temporal decay of the vortex line density in the grid-generated He II turbulence.