2008/10/20 by G. Boffetta, Antonio Celani, Boffetta, G. +10
Engineering · Physics and Astronomy · #Atomic and Subatomic Physics Research #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum, superfluid, helium dynamics #Spacecraft and Cryogenic Technologies #nlin.CD
paper · pdf · doi:10.48550/arxiv.0810.3573
7 pages, 2 figures
arxiv created 2008/10/20 · openalex publication_date 2008/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the double cascade of energy and wave action in a local model of superfluid vortex filaments. The model is obtained from a truncated expansion of the 2D Local Induction Approximation and it is shown to support six-wave interactions. We argue that, because of the uncertainty in the vortex core profile, this model has the same status of validity as the traditionally used Biot-Savart model with cutoff, but it has advantage of being much simpler. Our minimal model leads to a wave kinetic equation for which we predict existence of two distinct power-law scaling in the spectrum, corresponding to a direct cascade of energy and an inverse one of wave action. Direct numerical simulations confirm the theoretical predictions in the weak turbulence regime.