Vorticity filaments are characteristic structures of two-dimensional
turbulence. The
formation, persistence and effect of vorticity filaments are examined using
a
high-resolution direct numerical simulation (DNS) of the merging of two
positive Gaussian
vortices pushed together by a weaker negative vortex. Many intense spiral
vorticity
filaments are created during this interaction and it is shown using a wavelet
packet
decomposition that, as has been suggested, the coherent vortex stabilizes
the filaments.
This result is confirmed by a linear stability analysis at the edge of
the vortex and
by a calculation of the straining induced by the spiral structure of the
filament in the
vortex core. The time-averaged energy spectra for simulations using hyper-viscosity
and Newtonian viscosity have slopes of −3 and −4 respectively.
Apart
from a much higher effective Reynolds number (which accounts for the difference
in energy spectra), the hyper-viscous simulation has the same dynamics
as
the Newtonian
viscosity simulation. A wavelet packet decomposition of the hyper-viscous
simulation
reveals that after the merger the energy spectra of the filamentary
and coherent parts of the vorticity field have slopes of −2 and −6
respectively. An asymptotic analysis and DNS for weak external strain shows
that a circular filament at a distance R from
the vortex centre always reduces the deformation of a Lamb's
(Gaussian) vortex in
the region r[ges ]R. In the region r<R
the deformation is also reduced provided
the filament is intense and is in the vortex core, otherwise the
filament may slightly
increase the deformation. The results presented here should be useful for
modelling
the coherent and incoherent parts of two-dimensional turbulent flows.
Unfolding energy spectra of double-periodicity two-dimensional systems: Twisted bilayer graphene and
MoS2
on graphene
