0000000000378529
AUTHOR
Giuseppa Gaeta
Nonlinear evolution equations for turbulent superfluids
In this paper a system of evolution equations for turbulent superfluid helium is written in the nonlinear regime, choosing as fundamental fields the density, the velocity, the heat flux, the non-equilibrium temperature and the average vortex line density per unit volume. Approximate equations are written, where second order terms in the non-equilibrium quantities are retained.
Wave propagation in anisotropic turbulent superfluids
In this work, a hydrodynamical model of Superfluid Turbulence previously formulated is applied to study how the presence of a non-isotropic turbulent vortex tangle modifies the propagation of waves. Two cases are considered: wave front parallel and orthogonal to the heat flux. Using a perturbation method, the first-order corrections due to the presence of the vortex tangle to the speeds and to the amplitudes of the first and second sound are determined. It is seen that the presence of the quantized vortices couples first and second sound, and the attenuation of second sound is proportional to the line density L if the wave propagates orthogonal to the heat flux, while it is proportional to …
Propagation of fourth sound in turbulent superfluids via extended thermodynamics
The work deals with further developments of a study previously initiated, in which a macroscopic one-fluid model of inhomogeneous turbulent superfluids, based on extended thermodynamics, had been formulated. In this work the study is carried on. First the influence of the remnant vortices on the propagation of the first and second sound is studied. Then a boundary condition able to explain the reversible flow of superfluid flowing through a thin capillary is postulated and two vector fields, which have the dimensions of velocity and can be interpreted as the velocities of normal and superfluid components, are introduced. By using these new fields, a comparison between this model and the Hal…
Flow of turbulent superfluid helium inside a porous medium
The work deals with further developments of a study previously initiated, in which a macroscopic model of inhomogeneous superfluid turbulence, based on extended thermodynamics, has been formulated. The model choose as fundamental fields, beside the traditional fields, two extra variables: the averaged vortex line length per unit volume and the heat flux. Using this model the propagation of the fourth sound inside a superleak is investigated: it is shown that, if the configuration of the vortex tangle inside the superleak are not altered -on the average- by the presence of the walls, when the fourth sound is propagated, vibrations in the vortex line density are present, too.
A Continuum Theory of Superfluid Turbulence based on Extended Thermodynamics
A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is extended in this paper to nonlinear regimes. The theory chooses as fundamental fields the density, the velocity, the energy density, and two extra variables, in order to include the specific properties of the fluid in consideration: the averaged vortex line length per unit volume and a renormalized expression of the heat flux. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu method of Lagrange multipliers. Using a Legendre transformation, it is shown that the constitutive theory is determined by the choice of only two scalar f…
Far From Equilibrium Constitutive Relations in a Nonlinear Model of Superfluid Turbulence
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.
HYDRODYNAMICAL MODELS OF SUPERFLUID TURBULENCE
This review paper puts together some of our results concerning the application of non equilibrium Thermodynamics to superfluid liquid helium. Two of the most important situations of this quantum fluid are rotating superfluid and superfluid turbulence, both characterized by the presence of quantized vortices (vortex lines whose core is about 1 Angstrom and the quantum of circulation is $h/m$, $h$ being the Plank's constant and $m$ the mass of helium atom). In the first part of the work a non-standard model of superfluid helium, which considers heat flux as independent variable, is briefly recalled, and compared with the well known two-fluid model, in absence of vortices, proposed by Tisza an…
Extended Thermodynamics of Turbolent Superfluids:Nonlinear Costitutive Theory
In this paper we extend to nonlinear regimes a thermodynamical model of inhomogeneous superfluid turbulence previously formulated. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux and the averaged vortex line length per unit volume. The relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. Using a Legendre transformation, in the paper it is shown that the constitutive theory is determined by the choice of only two scalar functions of the intrinsic Lagrange multipliers.