Non-Oberbeck–Boussinesq zonal flow generation

Held, Markus; Wiesenberger, Matthias; Kube, Ralph; Kendl, A.

doi:10.1088/1741-4326/aad28e

Cited by 22 publications

(66 citation statements)

References 61 publications

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“…Retaining these density fluctuations does render the derivation and the final expressions more complicated though, but the Favre averages demonstrated in equation 6 allow to reduce the number of closure terms that appear in the mean-field equations with respect to using Reynolds averages shown in equation 4. Similar Favre averaging techniques have been used to take density fluctuations into account to analyse zonal flow generation by Held et al 28 .…”

Section: Derivation Of K ⊥ Equationmentioning

confidence: 99%

“…In more complex cases different saturation mechanisms might come into play though. For example, flow shear is believed to lead to turbulence quenching and may lead to zonal flow and transport barrier formation 26,28,37,38 . This phenomenon is not observed in this work as the electrostatic potential is very strongly constrained by the sheath potential such that no significant ExB flow in the diamagnetic y-direction and thus no flow shear can develop.…”

Section: Please Cite This Article Asmentioning

confidence: 99%

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Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

2021

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This paper studies the turbulent kinetic energy (k ⊥ ) in 2D isothermal electrostatic interchange-dominated ExB drift turbulence in the scrape-off layer, and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. Reynolds stress energy transfer also seems to be negligible, presumably because no significant shear flow develops under the given assumptions of isothermal sheath-limited conditions in the open field line region. The interchange source of the turbulence is analytically related to the average turbulent ExB energy flux, while a regression analysis of TOKAM2D data suggests a model that is linear in the turbulent kinetic energy for the sheath loss. A similar regression analysis yields a diffusive model for the average radial particle flux, in which the anomalous diffusion coefficient scales with the square root of the turbulent kinetic energy. Combining these three components, a closed set of equations for the mean-field particle transport is obtained, in which the source of the turbulence depends on mean flow gradients and k ⊥ through the particle flux, while the turbulence is saturated by parallel losses to the sheath. Implementation of this new model in a 1D mean-field code shows good agreement with the original TOKAM2D data over a range of model parameters.Recently, Bufferand et al. 19 proposed a mean-field model for the turbulent particle transport in the plasma edge that draws inspiration from these RANS models. More specifically, the model bears similarity to k(−ε) models, where equations for the turbulent kinetic energy k (and dissipation ε) are solved to provide time-and length scales to model the closure terms 18 . Bufferand et al. proposed a diffusive model for the radial particle transport where the anomalous trans-

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Section: Derivation Of K ⊥ Equationmentioning

confidence: 99%

Section: Please Cite This Article Asmentioning

confidence: 99%

Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

2021

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“…A paradigmatic model to study drift wave turbulence and zonal flow dynamics in the edge of magnetized fusion plas-mas is the Hasegawa-Wakatani (HW) model [28,56,29,50]. Recently, this model has been extended to include large relative density fluctuation amplitudes and steep density gradients within a full-F gyro-fluid approach, thus facilitating studies in the non-Oberbeck-Boussinesq regime [31]. The dimensionless modified full-F HW equations consists of continuity equations for electron particle density n, ion gyro-center density N and the polarisation equation The initial (gyro-center) density fields n( x, 0) = N( x, 0) = n G (x) 1 + δn 0 ( x) consist of the reference background density profile n G := e −κx , which is perturbed by a turbulent bath δn 0 ( x).…”

Section: Reproducibility In Numerical Simulationsmentioning

confidence: 99%

“…Here, κ parameterizes the constant background density gradient length. For further details to the model we refer the reader to Reference [31].…”

Section: Reproducibility In Numerical Simulationsmentioning

confidence: 99%

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Wiesenberger

Einkemmer

Held

et al. 2019

Computer Physics Communications

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Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two-and three-dimensional drift-and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique.We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. We briefly discuss alternative methods to ensure the correctness of results like the convergence of reduced physical quantities of interest, ensemble simulations, invariants or reduced simulation times.In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 10 −1 and 10 3 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak).

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“…1) Finally, we study how non-modality affects the turbulence intensity in collisional DW turbulence without and with zonal flows. Here, the underlying models are the NOB-extended OHW (equations (2), (1b) and (1c)) and modified HW (MHW) model [44], respectively. In Fig.…”

Section: B Non-modal Analysismentioning

confidence: 99%

The collisional drift wave instability in steep density gradient regimes

2019

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The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background density gradients. In this regime we report on corrections by factors of order one to the eigenvalue analysis of former OB approximated approaches as well as on spatially localised eigenfunctions, that contrast strongly with their OB approximated equivalent. Remarkably, non-modal phenomena arise for large density inhomogeneities and for all collisionalities. As a result, we find initial decay and non-modal growth of the free energy and radially localised and sheared growth patterns. The latter non-modal effect sustains even in the nonlinear regime in the form of radially localised turbulence or zonal flow amplitudes. II. GYRO-FLUID MODELOur analysis is based on an energetically consistent full-F gyro-fluid model [39], which is derived by taking the gyro-fluid moments over the gyro-kinetic Vlasov-Maxwell equations [40]. In order to ease the following

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Non-Oberbeck–Boussinesq zonal flow generation

Cited by 22 publications

References 61 publications

Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

The collisional drift wave instability in steep density gradient regimes

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