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 wave action up-scale via weakly nonlinear interactions, and this is the main mechanism of turbulence at scales less than the inter-vortex distance. In the case of an idealized 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) [B. V. Svistunov, Phys. Rev. B 52, 3647 (1995)] and a pure inverse cascade form -3 at k < k (0) (V. Lebedev, private communication). However, forcing produced by the reconnections contains a broad range of Fourier modes. What scaling should one expect in this case? An answer to this question has been obtained using the differential model for the Kelvin wave turbulence introduced in [S. Nazarenko, JETP Lett. 83, 198 (2005)]. 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.