On the investigation of properties of superfluid $^4$He turbulence using a hot-wire signal

We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.