Kelvin-wave turbulence generated by vortex reconnections
S. Nazarenko
Mathematics institute, University of Warwick, Coventry CV4 7AL, UK
PACS: 67.40.Vs
Abstract
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 k0, the turbulence spectrum exponent
has a
pure direct cascade form -17/5 at scales k>k0
[11naz-svist] and a pure inverse cascade form
-3 at k<k0 [11naz-leb]. 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 [11naz-naz_kelvin].
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.