A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence

Abstract We propose a mathematical interpolation between several regimes of energy cascade in quantum turbulence He II. On the basis physical interpretation such expression we discuss which conditions it is expected to appear an intermediate $k^{2}$ k 2 regime (equipartition regime) transition region hydrodynamic and Kelvin wave (namely, $k^{-5/3}$ − 5 / 3 $k^{-1}$ 1 regions coflow situations $k^{-3}$ counterflow situations). It seen that if rate transfer from sufficiently slow, equipartition will be present, but for higher values disappear. For high rates transfer, monotonous, characterized by negative exponent $k$ $-5/3$ −1 (or −3 −1), instead positive 2 regime.