Spontaneous angular momentum generation of two-dimensional fluid flow in an elliptic geometry

Keetels, GH Geert; Clercx, Hjh Herman; Heijst, van Gjf Gert-Jan

doi:10.1103/physreve.78.036301

Cited by 12 publications

(14 citation statements)

References 18 publications

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“…We note that a monopole distribution emerges at late times in the square domain for our neutral vortex gas. This causes the flow to spontaneously acquire a non-zero value of angular momentum defined as L = (r × ρu)d 2 x where r is measured relative to the centre of the domain as pointed out in [44,49,50] (see animations included in S1PVDipS and S1PVMonS). These results are consistent with the mean-field predictions which predict that a monopole distribution of vortices is the most probable state in the square and is, therefore, expected to emerge at long times in the latter stages of the simulation.…”

Section: Mean Field Theory Of Vortex Gasmentioning

confidence: 99%

Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium

Salman

Maestrini

2016

Phys. Rev. A

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We study the relaxation of a two-dimensional (2D) ultracold Bose gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large-scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Poisson-Boltzmann equation. The results allow us to characterize the spectral energy condensate in a 2D quantum fluid that bears striking similarity to similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum

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Section: Mean Field Theory Of Vortex Gasmentioning

confidence: 99%

Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium

Salman

Maestrini

2016

Phys. Rev. A

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“…In this case the flow relaxes to a state with or without angular momentum, depending on the shape of the domain [16][17][18]. Indeed in circular domains without initial angular momentum the flow generally relaxes to a state free from angular momentum [19], whereas as soon as the axi-symmetry is broken the flow relaxes to a state containing a domain filling structure, containing significant angular momentum [20]. Theoretical progress has been made to explain the phenomenon in the inviscid case, based on a model of interacting vortices [21][22][23].In the case of bounded two-dimensional MHD it is not known, up to now, to which kind of state the flow relaxes and this will be addressed in the present letter.…”

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confidence: 99%

Rapid Generation of Angular Momentum in Bounded Magnetized Plasma

2008

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Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in non-axisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a larger timescale, the generation of a magnetic angular momentum, or angular field, is observed. For axi-symmetric geometries, the generation of angular momentum is absent, nevertheless a weak angular field can be observed. The derived evolution equations for both angular momentum and angular field yield possible explanations for the observed behaviour.PACS numbers: 52.30. Cv, 52.65.Kj, The generation of large coherent structures of the size of the flow domain is a generic feature of two-dimensional (2D) turbulence. Indeed, due to the inverse energy cascade, 2D flows show a tendency to create space filling structures. The nature of these structures and the way they are produced vary from flow to flow. In the context of Navier-Stokes turbulence the generation of a largescale domain-filling structure was predicted by Kraichnan [1] and observed in the case of forced turbulence in a periodic domain in which energy condenses at the smallest possible wave number modes [2,3]. In forced wallbounded flows this was reproduced numerically [4] and experimentally [5], and it was shown that a large scale rotating structure emerges, which dramatically reduces the level of the turbulent fluctuations [6].A similar observation can be made in fusion plasmas, in which the dynamics share many features with 2D flows due to the imposed magnetic field. It is often assumed that in these plasmas large scale poloidal structures, called zonal flows, are beneficial for the confinement as they suppress turbulence and shear apart radially extended structures, which are largely responsible for anomalous transport [7][8][9]. The hereby created transport barriers might play a key role in the transition to an improved confinement state (H-mode) [10]. In the case of MHD turbulence the role of rotation was shown to have a similar effect on the flow, reducing the velocity fluctuations and hereby stabilizing the magnetic field [11]. In the present work we will continue the investigation of wall bounded non-ideal MHD. The generation of zonal flows through the absence of charge neutrality will not be addressed (charge neutrality being implied by the onefield MHD approximation). However, MHD allows for an affordable global description of non-uniform magnetoplasmas [12]. The present work could be related to the L-H transition through the beneficial effects of large scale poloidal rotation (which is observed in the present work) on the confinement of the plasma. The present study is also motivated by the observation that MHD-equilibria in toroidal geometry imply finite flow-fields due to the finite viscosity and resistivity [12][13][14]. In these works non-ideal MHD steady states were investigated in both the limit of small and large viscosity. In each case it was shown that the steady state contains non-vanishing velocity ...

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“…Further important developments along this direction were later carried out by Pointin and Lundgren [8][9][10]. The validity of the theory was subsequently tested against direct numerical simulations of classical fluids [11][12][13][14]. However, the use of point vortices to model a continuum vorticity field of a classical fluid was a contentious issue.…”

Section: Introductionmentioning

confidence: 99%

Entropy of Negative Temperature States for a Point Vortex Gas

Maestrini

Salman

2019

J Stat Phys

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We study the dynamics and statistical mechanical equilibria of a neutral two-dimensional point vortex gas with Coulomb-like interactions confined in a squared and a rectangular domain. Using a punctuated Hamiltonian model in which we model the process of vortexantivortex annihilation in superfluids by removing vortex dipoles, we show that this leads to evaporative heating of the system. Consequently, the vortex gas enters the negative temperature regime and subsequently relaxes to a maximum entropy configuration. We demonstrate that the large scale flows that emerge in this regime can be explained by using an equilibrium statistical mechanical mean field theory of point vortices based on a Poisson-Boltzmann equation. In particular, we observe that the emergent large scale flows in our point vortex simulations in the squared domain give rise to a spontaneous acquisition of angular momentum whereas the flows in the rectangular domain prefers a state with zero angular momentum. In addition to the observed qualitative agreement between the dynamical simulations and the theory that we demonstrate for the two geometries, we also present an approach that allows us to accurately compute a coarse-grained vorticity field, and henceforth recover the entropy from our dynamical runs. This allows us to perform a quantitative comparison between the dynamical point vortex simulations and the statistical mechanical predictions of the mean field theory thereby allowing us to clearly assert the validity of the assumptions of the statistical approaches as applied to this system with long-range interactions.

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Spontaneous angular momentum generation of two-dimensional fluid flow in an elliptic geometry

Cited by 12 publications

References 18 publications

Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium

Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium

Rapid Generation of Angular Momentum in Bounded Magnetized Plasma

Entropy of Negative Temperature States for a Point Vortex Gas

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