Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $\alpha (T)\ll 1$, responsible for the cutoff. The curve $\ln L(\ln \alpha )$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber regions. Excellent agreement with recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]–in which $L(T)$ has been measured down to $T\sim 0.08$K–implies that the scenario of low-temperature superfluid turbulence is now experimentally validated, and allows to quantify the Kelvin-wave cascade spectrum.