Statistics of turbulence and intermittency enhancement in superfluid He-4 counterflow

We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid He-4 counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum E-xz(k(y)) (averaged over the xz plane, parallel to the channel wall), directly measured as a function of the wall-normal wave vector k(y), gives more detailed information on the energy distribution over scales than the corresponding second-order structure function S-2(delta(y)). In particular, we discover two intervals of k(y) with different apparent exponents: E-xz(k(y)) alpha k(y)(-mC) for k less than or similar to k(x) and E-xz (k(y)) alpha k(y)(-mF) for k greater than or similar to k(x). Here k(x) denotes the wave number that separates scales with relatively strong (for k less than or similar to k(x)) and relatively weak (for k greater than or similar to k(x)) coupling between the normal-fluid and superfluid velocity components. We interpret these k ranges as cascade-dominated and mutual-friction-dominated intervals, respectively. The general behavior of the experimental spectra E-xz(k(y)) agrees well with the predicted spectra [L'vov and Pomyalov, Phys. Rev. B 97, 214513 (2018)]. Analysis of the nth-order structure functions statistics shows that in the energy-containing interval, the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade- and mutual-friction-dominated intervals, we found some modest enhancement of intermittency with respect to its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.