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 l(q)=2 pi(epsilon/kappa(3))(-1/4), where epsilon 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 kappa, for wave numbers k>k(q) identical with 2 pi/l(q). We propose that the spectral density in this range is of the form straight phi(k)=C epsilon kappa(-1)k(-3), where C is the three-dimensional Kolmogorov constant in classical turbulence. This form is consistent with recent experiments in the temperature range 1.2 K