An overview of the statistical properties of two-dimensional turbulence in fluids with particles, conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids

Pandit, Rahul; Banerjee, Debarghya; Bhatnagar, Akshay; Brachet, Marc; Gupta, A.; Mitra, Dhrubaditya; Pal, Nairita; Perlekar, Prasad; Ray, Samriddhi Sankar; Shukla, Vishwanath; Vincenzi, Dario

doi:10.1063/1.4986802

Cited by 37 publications

(28 citation statements)

References 230 publications

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“…Hyperviscosity has been used quite commonly in research papers studying turbulence in fluids and plasmas [25,26,27] using both direct numerical simulations and shell models. The use of hyperviscosity becomes absolutely essential for certain class of equations like the Hall MHD [28] equations where the non linearity has different dominant behaviour for smaller length scales.…”

Section: Discussionmentioning

confidence: 99%

Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

Banerjee

2019

Eur. Phys. J. B

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Energy spectrum of turbulent fluids exhibit a bump at an intermediate wavenumber, between the inertial and the dissipation range. This bump is called bottleneck. Such bottlenecks are also seen in the energy spectrum of the solutions of hyperviscous Burgers equation. Previous work, have shown that this bump corresponds to oscillations in real space velocity field. In this paper we present numerical and analytical results of how the bottleneck and its' real space signature, the oscillations, grow as we tune the order of hyperviscosity. We look at a parameter regime α ∈ [1, 2] where α = 1 corresponds to normal viscosity and α = 2 corresponds to hyperviscosity of order 2. We show that even for the slightest fractional increment in the order of hyperviscosity (α) bottlenecks show up in the energy spectrum.

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Section: Discussionmentioning

confidence: 99%

Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

Banerjee

2019

Eur. Phys. J. B

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“…The contribution by Pandit et al 17 presents an extensive review on the dynamics of complex two-dimensional fluids, including conducting fluids, fluids with inertial particles and polymer additives, binary mixtures, and superfluids.…”

Section: By G Falkovich G Boffetta and M Shatsmentioning

confidence: 99%

Introduction to Focus Issue: Two-Dimensional Turbulence

et al. 2017

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“…To do so, we make use of both the Gross-Pitaevskii equation (GPE) description of superfluids 36,37 and the suitably adapted classical treatment of point vortices in 2D. In our GPE description, we make use of a recently developed minimal model [38][39][40] , wherein we couple the equations of motion of particles with the GP classical wave function ψ. We demonstrate that the Magnus force description borrowed from the theory of ideal hydrodynamic flow works provides a good description of the dynamics of particle loaded vortices in superfluids.…”

Section: Introductionmentioning

confidence: 99%

Magnus-force model for active particles trapped on superfluid vortices

et al. 2020

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Experimentalists use particles as tracers in liquid helium. The intrusive effects of particles on the dynamics of vortices remain poorly understood. We implement a study of how basic well understood vortex states, such as a propagating pair of oppositely signed vortices, change in the presence of particles by using a simple model based on the Magnus force. We focus on the 2D case, and compare the analytic and semi-analytic model with simulations of the Gross-Pitaevskii (GP) equation with particles modelled by dynamic external potentials. The results confirm that the Magnus force model is an effective way to approximate vortex-particle motion either with closed-form simplified solutions or with a more accurate numerically solvable ordinary differential equations (ODEs). Furthermore, we increase the complexity of the vortex states and show that the suggested semi-analytical model remains robust in capturing the dynamics observed in the GP simulations.

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An overview of the statistical properties of two-dimensional turbulence in fluids with particles, conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids

Cited by 37 publications

References 230 publications

Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

Introduction to Focus Issue: Two-Dimensional Turbulence

Magnus-force model for active particles trapped on superfluid vortices

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