10,901 research outputs found
Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence
In two previous papers two evolution equations for the vortex line density
, proposed by Vinen, were generalized to rotating superfluid turbulence and
compared with each other. Here, the already generalized alternative Vinen
equation is extended to the case in which counterflow and rotation are not
collinear. Then, the obtained equation is considered from the viewpoint of
non-equilibrium thermodynamics. According with this formalism, the
compatibility between this evolution equation for and that one for the
velocity of the superfluid component is studied. The compatibility condition
requires the presence of a new term dependent on the anisotropy of the tangle,
which indicates how the friction force depends on the rotation rate.Comment: 18 pages, 3 figure
Waves propagation in turbulent superfluid helium in presence of combined rotation and counterflow
A complete study of the propagation of waves (namely longitudinal density and
temperature waves, longitudinal and transversal velocity waves and heat waves)
in turbulent superfluid helium is made in three situations: a rotating frame, a
thermal counterflow, and the simultaneous combination of thermal counterflow
and rotation. Our analysis aims to obtain as much as possible information on
the tangle of quantized vortices from the wave speed and attenuation factor of
these different waves, depending on their relative direction of propagation
with respect to the rotation vector.Comment: 17 pages, 2 figure
A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains
We study some convergence issues for a recent approach to the problem of
transparent boundary conditions for the Helmholtz equation in unbounded
domains. The approach is based on the minimization on an integral functional
which arises from an integral formulation of the radiation condition at
infinity. In this Letter, we implement a Fourier-Chebyschev collocation method
and show that this approach reduce the computational cost significantly. As a
consequence, we give numerical evidence of some convergence estimates available
in literature and we study the robustness of the algorithm at low and mid-high
frequencies
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
We study a new approach to the problem of transparent boundary conditions for
the Helmholtz equation in unbounded domains. Our approach is based on the
minimization of an integral functional arising from a volume integral
formulation of the radiation condition. The index of refraction does not need
to be constant at infinity and may have some angular dependency as well as
perturbations. We prove analytical results on the convergence of the
approximate solution. Numerical examples for different shapes of the artificial
boundary and for non-constant indexes of refraction will be presented
Transition to ballistic regime for heat transport in helium II
The size-dependent and flux-dependent effective thermal conductivity of
narrow capillaries filled with superfluid helium is analyzed from a
thermodynamic continuum perspective. The classical Landau evaluation of the
effective thermal conductivity of quiescent superfluid, or the Gorter-Mellinck
regime of turbulent superfluids, are extended to describe the transition to
ballistic regime in narrow channels wherein the radius is comparable to (or
smaller than) the phonon mean-free path in superfluid helium. To do so
we start from an extended equation for the heat flux incorporating non-local
terms, and take into consideration a heat slip flow along the walls of the
tube. This leads from an effective thermal conductivity proportional to
(Landau regime) to another one proportional to (ballistic regime). We
consider two kinds of flows: along cylindrical pipes and along two infinite
parallel plates.Comment: 16 page
Coupled normal fluid and superfluid profiles of turbulent helium II in channels
We perform fully coupled two--dimensional numerical simulations of plane
channel helium II counterflows with vortex--line density typical of
experiments. The main features of our approach are the inclusion of the back
reaction of the superfluid vortices on the normal fluid and the presence of
solid boundaries. Despite the reduced dimensionality, our model is realistic
enough to reproduce vortex density distributions across the channel recently
calculated in three--dimensions. We focus on the coarse--grained superfluid and
normal fluid velocity profiles, recovering the normal fluid profile recently
observed employing a technique based on laser--induced fluorescence of
metastable helium molecules.Comment: 26 pages, 8 Figures, accepted for publication in Phys. Rev.
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