Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

Recent advances in experimental techniques have made it possible to explore highly non-trivial short-wavelength physics of low-temperature superfluid turbulence. We analyze the transformation of the (quasi-)classical Kolmogorov cascade into the Kelvin-wave cascades on individual vortex lines at high enough wavenumbers, revealing a chain of three qualitatively distinct intermediate regimes, supported by local-induction motion of the vortex lines, and distinguished by specific reconnection mechanisms. On the basis of this scenario, we develop a theory of low-temperature cascade cutoff, which predicts a peculiar behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $\alpha(T) \ll 1$, responsible for the cutoff. Excellent agreement with a recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]---in which $L(T)$ has been measured down to $T \sim 0.08\,$K---validates our scenario and allows to quantify the Kelvin-wave cascade spectrum.