Search results for "SUPERFLUID TURBULENCE"
showing 10 items of 27 documents
Fractal dimension of superfluid turbulence : A random-walk toy model
2021
This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf 43}, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent pr…
Non-Equilibrium Thermodynamics of Unsteady Superfluid Turbulence in Counterflow and Rotating Situations
2005
The methods of nonequilibrium thermodynamics are used in this paper to relate an evolution equation for the vortex line density $L$, describing superfluid turbulence in the simultaneous presence of counterflow and rotation, to an evolution equation for the superfluid velocity ${\mathbf{v}}_{s}$, in order to be able to describe the full evolution of ${\mathbf{v}}_{s}$ and $L$, instead of only $L$. Two alternative possibilities are analyzed, related to two possible alternative interpretations of a term coupling the effects of the counterflow and rotation on the vortex tangle, and which imply some differences between situations where counterflow and rotation vectors are parallel or orthogonal …
Far From Equilibrium Constitutive Relations in a Nonlinear Model of Superfluid Turbulence
2009
In this paper the complete nonlinear far from equilibrium constitutive theory in a non standard model of superfluid turbulence is studied and the consequences of all the relations obtained using the Liu method of Lagrange multipliers are investigated.
Second sound propagation in laminar and turbulent superfluid 4He via extended thermodynamics
2012
In this work, previous results on the complex propagation of second sound in laminar and turbulent superfluid 4He are reported. Furthermore the case of inhomogeneous superfluid turbulence is examined and, in particular, the wave propagation is investigated in the presence of an anisotropic vortex tangle. Two cases of physical interest are considered: wave front collinear and orthogonal to the heat flux.
Nonlocal and rotational effects in superfluid turbulence
2008
We discuss phenomenological equations for the evolution of vortex tangle in counterflow superfluid turbulence, which takes into account the influence of the non local effects, both in absence and in the presence of rotation.
Statistical mechanics and thermodynamics of turbulent quantum vortex tangles
2010
In this paper we present some phenomenological ideas about the thermodynamics of quantized vortex loops arising in superfluid turbulence. The system of vortex loops may be seen as a dissipative structure, not existing on its own but only under the influence of an external heat flux. Starting from a simple definition of the temperature of the vortex tangle and from the relation between energy and vortex length, we obtain the entropy of the system, as well as the caloric and thermal equations of state, relating internal energy and pressure to temperature and volume. We discuss the connection between our macroscopic results and microscopic results on vortex length distribution function having …
Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature
2010
By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. F…
Non-Equilibrium Thermodinamic analysis of rotating counterflow superfluid turbulence
2008
Two alternative evolution equations for the vortex line density L in counterflow superfluid turbulence in 4He were proposed by Vinen in 1958. These equations was recently generalized to counterflow superfluid turbulence in rotating containers. Here, according with the formalism of Non-Equilibrium Thermodynamics, the compatibility between the alternative Vinen equation as evolution equation for the vortex line density in rotating counterflow turbulence and the velocity of the superfluid component is studied. From the compatibility request a new term dependent on the anisotropy of the tangle arises.
Study of the anisotropy in turbulent superfluids
2010
In this review we are interested on the anisotropy and polarity of superfluid turbulence in helium II, a still open problem which needs more details. Though some of the results presented here have already been published in different papers, this short review aims to put the main results together and to extend them when necessary. From the mesoscopic viewpoint, an evolution equation for the vortex line density was proposed in rotating counterflow (heat flux without mass flux) by means of dimensional analysis. Then, starting from the microscopic viewpoint this evolution equation was further extended to include situations where turbulence is not homogeneously distributed. Indeed, microscopical…
Stability in the plane Couette flow of superfluid helium
2009
An hydrodynamical model previously proposed to describe the presence of vortices in counterflow superfluid turbulence and in rotating containers is used to discuss plane Couette flow and the stability of the stationary solution.