Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

Saluto, Lidia; Mongiovı̀, Maria Stella

doi:10.1515/caim-2016-0010

Cited by 3 publications

(4 citation statements)

References 31 publications

(66 reference statements)

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“…The impact of the diffusion flux was studied in a recent work by Saluto et al [11]. The authors observed that the influence of the vortex diffusion is focused on the local values of L(y) rather than on the form of the spatial distribution VLD.…”

Section: Vortex-line Density Fluxmentioning

confidence: 99%

“…One of serious problems, is the application of the Vinen theory to complicated situations, in particular to inhomogeneous flows (for recent papers see e.g. [8], [9], [10], [11], [12]). In the cited papers the authors, analyzing numerically the steady counterflowing helium in an inhomogeneous channel flow, obtained a very specific behavior of the VLD L(r, t), which cannot be interpreted in terms of equation (1).…”

Section: Introductionmentioning

confidence: 99%

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Nonuniform quantum turbulence in superfluids

Nemirovskii

2018

Phys. Rev. B

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The problem of quantum turbulence in a channel with an inhomogeneous counterflow of superfluid turbulent helium is studied. The counterflow velocity V x ns (y) along the channel is supposed to have a parabolic profile in the transverse direction y. Such statement corresponds to the recent numerical simulation by Khomenko et al. [Phys. Rev. B 91, 180504 (2015)]. The authors reported about a sophisticated behavior of the vortex line density (VLD) L(r, t), different from L ∝ V x ns (y) 2 , which follows from the naive, straightforward application of the conventional Vinen theory. It is clear, that Vinen theory should be refined by taking into account transverse effects and the way it ought to be done is the subject of active discussion in the literature. In the work we discuss several possible mechanisms of the transverse flux of VLD L(r, t) which should be incorporated in the standard Vinen equation to describe adequately the inhomogeneous quantum turbulence (QT). It is shown that the most effective among these mechanisms is the one that is related to the phase slippage phenomenon. The use of this flux in the modernized Vinen equation corrects the situation with an unusual distribution of the vortex line density, and satisfactory describes the behavior L(r, t) both in stationary and nonstationary situations. The general problem of the phenomenological Vinen theory in the case of nonuniform and nonstationary quantum turbulence is thoroughly discussed.

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Section: Vortex-line Density Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonuniform quantum turbulence in superfluids

Nemirovskii

2018

Phys. Rev. B

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“…Note that in general the vortex flux can also contain other terms 8 , for example a diffusive component 21,22 ; however if the tangle is polarised, as in the case of counterflow or rotating turbulence, these terms are expected to be negligible. Nevertheless, in particular geometries 24 they may become important.…”

Section: The Equation For the Anisotropy Parametermentioning

confidence: 99%

Dynamics of the vortex line density in superfluid counterflow turbulence

et al. 2018

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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 L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides L and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter I l0 . Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter I l0 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.

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“…Normally, heat flow in He II is considered in longitudinal tubes with constant cross section. However, we have also focused a part of our analyses in inhomogeneous situations where L changes with position [37]. An especially, relevant and simple situation is that of cylindrical radial flows [29,30,37], which is relevant, for instance, in the cooling of cylindrical systems through superfluid helium.…”

Section: Heat Rectification In Radial Turbulent Flowmentioning

confidence: 99%

Heat rectification in He II counterflow in radial geometries

Saluto

Jou

Mongiovı̀

2018

Communications in Applied and Industrial Mathematics

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We consider heat rectification in radial flows of turbulent helium II, where heat flux is not described by Fourier's law, but by a more general law. This is different from previous analyses of heat rectification, based on such law. In our simplified analysis we show that the coupling between heat flux and the gradient of vortex line density plays a decisive role in such rectification. Such rectification will be low at low and high values of the heat rate, but it may exhibit a very high value at an intermediate value of the heat rate. In particular, for a given range of values for the incoming heat ow, the outgoing heat flow corresponding to the exchange of internal and external temperatures would be very small. This would imply difficulties in heat removal in a given range of temperature gradients.

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Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

Cited by 3 publications

References 31 publications

Nonuniform quantum turbulence in superfluids

Nonuniform quantum turbulence in superfluids

Dynamics of the vortex line density in superfluid counterflow turbulence

Heat rectification in He II counterflow in radial geometries

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