96 research outputs found
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
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
The saturation of decaying counterflow turbulence in helium II
We are concerned with the problem of the decay of a tangle of quantized
vortices in He II generated by a heat current. Direct application of Vinen's
equation yields the temporal scaling of vortex line density .
Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf
44}, 7563 (1991)] observed a faster decay followed by a slower decay. More
recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found
an initial transient followed by the same classical scaling observed
in the decay of grid-generated turbulence. We present a simple theoretical
model which, we argue, contains the essential physical ingredients, and
accounts for these apparently contradictory results.Comment: 19 pages, 5 figure
Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics
In this paper we show that a recent hydrodynamical model of superfluid
turbulence describes vortex density waves and their effects on the speed of
high-frequency second sound. In this frequency regime, the vortex dynamics is
not purely diffusive, as for low frequencies, but exhibits ondulatory features,
whose influence on the second sound is here explored.Comment: 8 page
Effective thermal conductivity of helium II: from Landau to Gorter-Mellink regimes
The size-dependent and flux-dependent effective thermal conductivity of
narrow channels filled with He II is analyzed. The classical Landau evaluation
of the effective thermal conductivity of quiescent He II is extended to
describe the transition to fully turbulent regime, where the heat flux is
proportional to the cubic root of the temperature gradient (Gorter-Mellink
regime). To do so we use an expression for the quantum vortex line density
in terms of the heat flux considering the influence of the walls. From it, and
taking into account the friction force of normal component against the
vortices, we compute the effective thermal conductivity
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
Test of Information Theory on the Boltzmann Equation
We examine information theory using the steady-state Boltzmann equation. In a
nonequilibrium steady-state system under steady heat conduction, the
thermodynamic quantities from information theory are calculated and compared
with those from the steady-state Boltzmann equation. We have found that
information theory is inconsistent with the steady-state Boltzmann equation.Comment: 12 page
Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles
We include the effects of anisotropy and polarization in the hydrodynamics of
inhomogeneous vortex tangles, thus generalizing the well known
Hall-Vinen-Bekarevich-Khalatnikov equations, which do not take them in
consideration. These effects contribute to the mutual friction force between normal and superfluid components and to the vortex tension
force . These equations are complemented by an evolution
equation for the vortex line density , which takes into account these
contributions. These equations are expected to be more suitable than the usual
ones for rotating counterflows, or turbulence behind a cylinder, or turbulence
produced by a grid of parallel thin cylinders towed across a superfluid,
because in these situations polarization is expected to play a relevant role.Comment: 21 page
Dynamics of the vortex line density in superfluid counterflow turbulence
Describing superfluid turbulence at intermediate scales between the
inter-vortex distance and the macroscale requires an acceptable equation of
motion for the density of quantized vortex lines . The closure of such
an equation for superfluid inhomogeneous flows requires additional inputs
besides and the normal and superfluid velocity fields. In this paper
we offer a minimal closure using one additional anisotropy parameter .
Using the example of counterflow superfluid turbulence we derive two coupled
closure equations for the vortex line density and the anisotropy parameter
with an input of the normal and superfluid velocity fields. The
various closure assumptions and the predictions of the resulting theory are
tested against numerical simulations.Comment: 7 pages, 5 figure
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