Hydrodynamical model of anisotropic, polarized turbulent superfluids. I: Constraints for the fluxes
type: Item
instance of: scholarly article
title: Hydrodynamical model of anisotropic, polarized turbulent superfluids. I: Constraints for the fluxes
zbMATH Open document ID: 1395.82266
author: Liliana Restuccia
author: Maria Stella Mongiovì
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2018-04-11T00:00:00Z
review text: The paper is devoted to building up a hydrodynamical model of turbulence in liquid helium II, taking into account the polarization and anisotropy of the vortex tangle according with test results and numerical simulation. As fundamental variables in the one-fluid model of liquid helium II (in absence of vortices) density, velocity and absolute temperature are selected. At the same time, the heat flux is used as an internal variable describing the dynamics of the excitations. Three macroscopic quantities of the model are: (i) the average length of the vortex line per unit volume (vortex line density), which describes only the vortex tangle in a rotating sample and in well-developed counterflow superfluid turbulence; (ii) a pseudovector (axial vector), which describes the polarization of the vortex tangle; (iii) an asymmetric tensor, which models the anisotropy of the vortex tangle inside the considered particle. The goal of the paper is to formulate evolution equations for the three internal variables describing scalar, deviatoric and antisymmetric parts of a vorticity tensor and its acting behavior. With this aim, in the framework of extended thermodynamics with internal variables, the authors develop a (coarse grained) hydrodynamical model of liquid helium II, taking into account the presence of a polarized anisotropic tangle of quantized vortices. The evolution equations for the state variables are obtained starting from the balance equations of mass momentum and energy complemented in further evolution equations for the internal variables describing the dynamics of elementary excitations and the vortex tangle. Then the constraints on the constitutive quantities are deduced from the second law of thermodynamics, using the Liu method of Lagrange multipliers. It is deduced that the Lagrange multipliers are the partial derivatives of the entropy density in terms of their respective conjugated thermodynamic variables. Then, it is shown that the stress tensor is indepen…
reviewed by: Ivan A. Parinov
Mathematics Subject Classification ID: 82D50
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 35G15
zbMATH DE Number: 6858243
zbMATH Keywords: quantum turbulence
zbMATH Keywords: quantized vortices
zbMATH Keywords: inhomogeneous vortex tangle
zbMATH Keywords: anisotropic and polarized turbulence
MaRDI profile type: Publication
full work available at URL: s00033-017-0893-6
OpenAlex ID: W2772032890
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Wikidata QID: Q125657810
DOI: 10.1007/S00033-017-0893-6
description: scientific article; zbMATH DE number 6858243