A unified theory of zonal flow shears and density corrugations in drift wave turbulence

Singh, Rameswar; Diamond, P. H.

doi:10.1088/1361-6587/abd618

Cited by 22 publications

(36 citation statements)

References 70 publications

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“…Using (18) and (19) with the assumption that ∂ t χ ± k ≈ 0 q /dt appears to oscillate wildly, since its amplitude χ − q is vanishingly small, as can be seen in figure 4, these oscillations are not important for the rest of the dynamics. and ∂ t φ ± k = −ω ± k,nl is a constant, we obtain the nonlinear frequency shift, i.e.…”

Section: B Phase Evolutionmentioning

confidence: 95%

“…The phases of wave-number nodes in Hasegawa-Wakatani turbulence evolve according to (19) or written explicitly as (22). This suggests that one can possibly define some kind of order parameter for this system.…”

Section: B Triad Networkmentioning

confidence: 99%

“…The model is well known to generate high levels of large scale zonal flows, especially for C 1 [8][9][10]. It has been studied in detail for many problems in fusion plasmas including dissipative drift waves in tokamak edge [11,12], subcritical turbulence [13], trapped ion modes [14], intermittency [15,16], closures [17][18][19], feedback control [20], information geometry [21] and machine learning [22]. Variations of the Hasegawa-Wakatani model are regularly used for describing turbulence in basic plasma devices [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Gürcan¹,

Anderson²,

Moradi³

et al. 2022

Preprint

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Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking where the phase differences between dominant modes converge to constant values as individual phases increase in time. This allows the system to have approximately constant amplitude solutions. Non-resonant triads show similar behavior only when one of its legs is a zonal wave number. However when an additional triad, which is a reflection of the original one with respect to the y axis is included, the behavior of the resulting triad pair is shown to be more complex. In particular, it is found that triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy to the subdominant mode which keeps growing exponentially, while those involving larger radial wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay to zero). In order to study the dynamics in a connected network of triads, a network formulation is considered including a pump mode, and a number of zonal and non-zonal subdominant modes as a dynamical system. It was observed that the zonal modes become clearly dominant only when a large number of triads are connected. When the zonal flow becomes dominant as a 'collective mean field', individual interactions between modes become less important, which is consistent with the inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation is discussed for the same parameters and various forms of the order parameter are computed. It is observed that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function of scale in direct numerical simulations.

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Section: B Phase Evolutionmentioning

confidence: 95%

Section: B Triad Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Gürcan¹,

Anderson²,

Moradi³

et al. 2022

Preprint

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“…Applications include the investigation of turbulence in geophysical flows (Nazarenko & Quinn 2009) and magnetically confined plasmas (Horton 1999; Fujisawa et al. 2004), and more generally the characterization of self-organized turbulent states and zonal flows (Diamond, Hasegawa & Mima 2011; Singh & Diamond 2021).…”

Section: Introductionmentioning

confidence: 99%

A generalized Hasegawa–Mima equation in curved magnetic fields

Sato

Yamada

2022

J. Plasma Phys.

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We derive a model equation describing electrostatic plasma turbulence in general (inhomogeneous and curved) magnetic fields by analysing the effect of curved geometry on the ion fluid polarization drift velocity. The derived nonlinear equation generalizes the Hasegawa–Mima equation governing drift wave turbulence in a straight homogeneous magnetic field, and may serve as a toy model for the description of turbulent plasmas. The equation is most appropriate for configurations with a small $\boldsymbol {E}\times \boldsymbol {B}$ drift velocity divergence, or a mild spatial change in $\boldsymbol {E}\times \boldsymbol {B}$ drift velocity. We identify the conserved energy of the system, and obtain conditions on magnetic field topology for conservation of generalized enstrophy. Through numerical examples, we further show how the curvature of the magnetic field reshapes self-organized steady turbulent states.

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“…Another model, based on stochastic noise due to turbulence was proposed in Ref. [18]. The rest of this article is organized as follows: In Section 2, we describe the Lotka-Volterra Predator-Prey model, and we derive its time-dependent solution analytically.…”

Section: Introductionmentioning

confidence: 99%

Limit Cycle Oscillations, response time and the time-dependent solution to the Lotka-Volterra Predator-Prey model

Leconte,

Masson,

2021

Preprint

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In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations (LCO), and also for the response time between predator and prey population. These results are applied to the predator-prey interaction of zonal density corrugations and turbulent particle flux in gyrokinetic simulations of collisionless trapped-electron model (CTEM) turbulence. In the turbulence simulations, the response time is shown to increase when approaching the linear threshold, and the same trend is observed in the Lotka-Volterra model.

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A unified theory of zonal flow shears and density corrugations in drift wave turbulence

Cited by 22 publications

References 70 publications

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

A generalized Hasegawa–Mima equation in curved magnetic fields

Limit Cycle Oscillations, response time and the time-dependent solution to the Lotka-Volterra Predator-Prey model

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