Kelvin-wave turbulence generated by vortex reconnections

Reconnections of quantum vortex filaments create sharp bends which degenerate into propagating Kelvin waves. These waves cascade their energy down-scale and their waveaction up-scale via weakly nonlinear interactions, and this is the main mechanism of turbulence at the scales less than the inter-vortex distance. In case of an idealised forcing concentrated around a single scale $k_0$, the turbulence spectrum exponent has a pure direct cascade form $-17/5$ at scales $k>k_0$ and a pure inverse cascade form $-3$ at $k<k_0$. However, forcing produced by the reconnections contains a broad range of Fourier modes. What scaling should one expect in this case? In this Letter I obtain an answer to this question using the differential model for the Kelvin wave turbulence introduced in. The main result is that the direct cascade scaling dominates, i. e. the reconnection forcing is more or less equivalent to a low-frequency forcing.