Dynamical scaling law in the development of drift wave turbulence

Watanabe, Takeshi; Fujisaka, Hirokazu; Iwayama, Takahiro

doi:10.1103/physreve.55.5575

Cited by 33 publications

(26 citation statements)

References 15 publications

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“…The two power laws in the frequency spectra seen in Fig. 8 are also consistent with the results of numerical simulations of the Hasegawa-Mima turbulence which give [11][12][13]:…”

Section: Zonal Flows and Turbulence In Plasmasupporting

confidence: 77%

Spectrally Condensed Fluid Turbulence and L-H Transitions in Plasma

Shats

Xia

2009

Plasma and Fusion Research

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Recent experimental and theoretical studies of two-dimensional (2D) turbulence reveal that spectrally condensed turbulence which is a system of coupled large-scale coherent flow and broadband turbulence, is similar to plasma turbulence near the L-H transition threshold. Large condensate vortices fed via the turbulent inverse energy cascade, can control both the level of the broadband turbulence by shear decorrelation, and the energy injected into turbulence at the forcing scale via sweeping of the forcing-scale vortices. The interaction between these ingredients of spectrally condensed fluid turbulence is in many aspects similar to the interactions in the zonal flow-GAMs-turbulence system in plasma. In this paper we overview recent results on condensed 2D turbulence and present evidence of interaction between its three components: condensate structures, turbulence and forcingscale vortices. This is compared with the modifications in the spectra of plasma electrostatic potential during L-H transitions. It is shown that mean zonal flows are spatially and temporally correlated with both the broadband turbulence and with the narrow spectral range identified as the spectral range of the underlying instability.

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“…The two power laws in the frequency spectra seen in Fig. 8 are also consistent with the results of numerical simulations of the Hasegawa-Mima turbulence which give [11][12][13]:…”

Section: Zonal Flows and Turbulence In Plasmasupporting

confidence: 77%

Spectrally Condensed Fluid Turbulence and L-H Transitions in Plasma

Shats

Xia

2009

Plasma and Fusion Research

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“…In this section, the scaling laws for quasi-geostrophic turbulence governed by this equation are briefly summarized. See Watanabe et al (1997Watanabe et al ( , 1998 for detailed derivation. In this system, the total energy E and the total enstrophy Q defined as 1 The scaling law for the energy spectrum in the energy-cascade region is…”

Section: Scaling Laws For Quasi-geostrophic Turbulencementioning

confidence: 99%

“…The studies by Watanabe et al (1997Watanabe et al ( , 1998 consider the finite Rossby's radius of deformation. (Their original motivation is to investigate quasi two-dimensional electric potential vertical to a magnetic field, but their basic equation, which is called the Charney-Hasegawa-Mima equation, is completely an equivalent of the quasi-geostrophic potential vorticity equation.)…”

Section: Introductionmentioning

confidence: 99%

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

Iga

Watanabe

2003

Journal of the Meteorological Society of Japan

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When a problem without viscosity is considered as an ideal case, a small dissipation term is necessary in many numerical calculations. Quasi-geostrophic turbulence, which is described by the barotropic version of quasi-geostrophic potential vorticity equation, (also called Charney-Hasegawa-Mima equation as an equivalent) is one of these situations: a dissipation term must be added in order to prevent the energy from piling up in the large wavenumber region. Consequently, the total energy decreases gradually, which should be conserved in an ideal situation. In this article, the total energy dissipation rate in quasi-geostrophic turbulence is estimated, based on the assumption that the energy dissipated in this system is equal to the energy transported to the large wavenumber region. This estimation complements the dynamic scaling laws for the quasi-geostrophic turbulence developed by Watanabe et al. (1998): the parameter expressing the total energy dissipation, which was determined from the result of the numerical calculation in their study, is derived from the parameters of the setting of the numerical calculation. This estimation also suggests the means to determine the appropriate artificial hyperviscosity coefficient used in numerical simulations.

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“…This situation is similar to energy transfer in the wave number space, so that in the spin turbulence it has a possibility to have constant energy flux for the spin-dependent interaction energy. From this consideration, we apply the Kolmogorov-type scaling analysis [168,169] into Eq. (146).…”

Section: Derivation Of the −7/3 Power Lawmentioning

confidence: 99%

Numerical Studies of Quantum Turbulence

2017

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We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose-Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross-Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed in revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose-Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates e.g. two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, etc., some of which has not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally we discuss open problems.

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Dynamical scaling law in the development of drift wave turbulence

Cited by 33 publications

References 15 publications

Spectrally Condensed Fluid Turbulence and L-H Transitions in Plasma

Spectrally Condensed Fluid Turbulence and L-H Transitions in Plasma

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

Numerical Studies of Quantum Turbulence

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