Coherent structures in ion temperature gradient turbulence-zonal flow

Singh, Rameswar; Singh, Raghvendra; Kaw, P. K.; Gürcan, Ö. D.; Diamond, P. H.

doi:10.1063/1.4898207

Cited by 18 publications

(34 citation statements)

References 53 publications

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“…Our main findings are as follows. (i) Contrary to the traditional WKE (tWKE) of the drifton dynamics, which predicts [12][13][14] nonlinear structures à la Bernstein-Greene-Kruskal (BGK) waves [26], the iWKE predicts that driftons do not have to be just passing or trapped. Instead, they can accumulate in certain spatial locations while experiencing indefinite growth of their momenta.…”

Section: Introductionmentioning

confidence: 98%

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability

2018

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The phase space of driftons (drift-wave quanta) is studied within the generalized Hasegawa-Mima collisionless-plasma model in the presence of zonal flows. This phase space is made intricate by the corrections to the drifton ray equations that were recently proposed by Parker [J. Plasma Phys. 82, 595820602 (2016)] and Ruiz et al. [Phys. Plasmas 23, 122304 (2016)]. Contrary to the traditional geometrical-optics (GO) model of the drifton dynamics, it is found that driftons can be not only trapped or passing, but they can also accumulate spatially while experiencing indefinite growth of their momenta. In particular, it is found that the Rayleigh-Kuo threshold known from geophysics corresponds to the regime when such "runaway" trajectories are the only ones possible. On one hand, this analysis helps visualize the development of the zonostrophic instability, particularly its nonlinear stage, which is studied here both analytically and through wave-kinetic simulations. On the other hand, the GO theory predicts that zonal flows above the Rayleigh-Kuo threshold can only grow; hence, the deterioration of intense zonal flows cannot be captured within a GO model. In particular, this means that the so-called tertiary instability of intense zonal flows cannot be adequately described within the quasilinear wave kinetic equation, contrary to some previous studies.

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Section: Introductionmentioning

confidence: 98%

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability

2018

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“…There exists a vast literature of QL WKE-based models of DW-ZF interactions. These models, which are called "improved WKE" (iWKE) by Zhu et al (2018a,b) and "CE2-GO" by Parker (2016Parker ( , 2018 Diamond et al 1994;Kim & Diamond 2003;Kaw et al 2002;Trines et al 2005;Singh et al 2014) with Ω = k x U − βk y /k 2 D and Γ = 0 . This simpler WKE-based model is referred as the "traditional WKE" (tWKE) in Ruiz et al (2016), Zhu et al (2018c,a,b), and Parker (2018).…”

Section: Comparison With Quasilinear Models and Weak Turbulence Theorymentioning

confidence: 99%

“…In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in literature. Singh et al 2014). The WKE has the intuitive form of the Liouville equation for the DW action density J in the ray phase space (Parker 2016;Ruiz et al 2016;Zhu et al 2018c;Parker 2018; Zhu et al 2018a,b):where Ω is the local DW frequency, Γ is a dissipation rate due to interactions with ZFs, and {·, ·} is the canonical Poisson bracket.…”

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confidence: 99%

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

2019

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The formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave-wave collisions. Hence, some important effects such as the Batchelor-Kraichnan inverse-energy cascade are not captured within this approach. Here we derive a wave kinetic equation that includes a DW collision operator in the presence of zonal flows. Our derivation makes use of the Weyl calculus, the quasinormal statistical closure, and the geometrical-optics approximation. The obtained model conserves both the total enstrophy and energy of the system. The derived DW collision operator breaks down at the Rayleigh-Kuo threshold. This threshold is missed by homogeneous-turbulence theory but expected from a full-wave quasilinear analysis. In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in literature. Singh et al. 2014). The WKE has the intuitive form of the Liouville equation for the DW action density J in the ray phase space (Parker 2016;Ruiz et al. 2016;Zhu et al. 2018c;Parker 2018; Zhu et al. 2018a,b):where Ω is the local DW frequency, Γ is a dissipation rate due to interactions with ZFs, and {·, ·} is the canonical Poisson bracket. (For the sake of clarity, terms related to external forcing and dissipation are omitted here.) However, as with all QL models, Eq. (1.1) neglects nonlinear wave-wave scattering, and in consequence, is not able to capture the Batchelor-Kraichnan inverse-energy cascade (Srinivasan & Young 2012) or produce the Kolmogorov-Zakharov spectra for DWs (Connaughton et al. 2015). Hence, a question remains as to whether the existing WKE for inhomogeneous turbulence can be complemented with a wave-wave collision operator C[J, J]. The goal of this work is to calculate C[J, J] explicitly. Starting from the generalized Hasegawa-Mima equations (gHME) (Krommes & Kim 2000; Smolyakov & Diamond 1999), we derive a WKE with a DW collision operator C[J, J] for inhomogeneous DW turbulence. Our derivation is based on the Weyl calculus (Weyl 1931), which makes our approach similar to that in Ruiz et al. (2016) where the QL approximation was used. However, in contrast to Ruiz et al. (2016), we do not rely on the QL approximation here but instead account for DW collisions perturbatively using the quasinormal approximation. The main result of this work are Eqs. (4.12) and (4.22). In this final result, DWs are modeled in a similar manner as in Eq. (1.1). The difference is that Eq. (4.12) includes nonlinear DW scattering, which is described by a wave-wave collision operator C[J, J] that is bilinear in the DW wave-action density J. The resulting model conserves the two nonlinear invariants of the gHME, which are the total enstrophy and the total energy. The present formulation is fundamentally different from the previously reported homogeneous weak-wave-turbulence mode...

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“…In fact, the retention of m = 2 demands for the equations for m = 3 and so on, which continues up to infinity. This closure problem, and its possible resolutionwill be discussed in a future publication [31]. The nonlinear terms on the right hand side acting as source/sink are poloidally asymmetric turbulent particle flux, poloidal momentum flux (i.e.…”

Section: Geodesic Acoustic Modementioning

confidence: 99%

“…However we believe that this agreement is incidental since it breaks down when higher harmonics (m = 2 etc.) are included in the calculation [30,31]. The agreement also breaks down on self consistent inclusion of n , T i,e responses on the GAM dispersion for m = 1.…”

Section: Introductionmentioning

confidence: 99%

Geodesic acoustic modes in a fluid model of tokamak plasma: the effects of finite beta and collisionality

Singh

Storelli

Gürcan

et al. 2015

Plasma Phys. Control. Fusion

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Starting from the Braginskii equations, relevant for the tokamak edge region, a complete set of nonlinear equations for the geodesic acoustic modes (GAM) has been derived which includes collisionality, plasma beta and external sources of particle, momentum and heat. Local linear analysis shows that the GAM frequency increases with collisionality at low radial wave number k r and decreases at high k r . GAM frequency also decreases with plasma beta. Radial profiles of GAM frequency for two Tore Supra shots, which were part of a collisionality scan, are compared with these calculations. Discrepency between experiment and theory is observed, which seems to be explained by a finite k r for the GAM when flux surface averaged density n and temperature T are assumed to vanish. It is shown that this agreement is incidental and self-consistent inclusion of n and T responses enhances the disagreement more with k r at high k r . So the discrepancy between the linear GAM calculation, (which persist also for more "complete" linear models such as gyrokinetics) can probably not be resolved by simply adding a finite k

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Coherent structures in ion temperature gradient turbulence-zonal flow

Cited by 18 publications

References 53 publications

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

Geodesic acoustic modes in a fluid model of tokamak plasma: the effects of finite beta and collisionality

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