Statistical properties of superfluid turbulence in He 4 from the Hall-Vinen-Bekharevich-Khalatnikov model

Verma, AK and Shukla, S and Shukla, V and Basu, A and Pandit, R (2023) Statistical properties of superfluid turbulence in He 4 from the Hall-Vinen-Bekharevich-Khalatnikov model. In: Physical Review E, 108 (4).

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Abstract

We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid turbulence in helium (He4) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analytical studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) P(γ), of the ratio γ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as P(γ)�γ3, for γ�1, and P(γ)�γ-3, for γ�1. Furthermore, we show that the PDF P(θ) of the angle θ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: P(θ)�θ for θ�θ� and P(θ)�θ-4 for θ��θ�1, where θ� is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, as well as the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature T, by using the experimentally determined mutual-friction coefficients for superfluid helium He4, so our results are of direct relevance to superfluid turbulence in this system. © 2023 American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review E
Publisher:	American Physical Society
Additional Information:	The copyright for this article belongs to author.
Keywords:	Distribution functions; Friction; Turbulence, Direct-numerical-simulation; Functional approach; Mutual friction; Normal-fluid velocity; Numerical simulation studies; Probability distribution functions; Statistical properties; Superfluid turbulence; Superfluid velocity; Von Karman, Superfluid helium, helium, article; clinical article; controlled study; friction; human; probability; simulation; steady state; temperature; velocity
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	04 Mar 2024 09:15
Last Modified:	04 Mar 2024 09:15
URI:	https://eprints.iisc.ac.in/id/eprint/84258

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