Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit

The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. Characteristically, this range exhibits a complex pattern of transient zonal evolution before a stable profile can arise. Nevertheless, the Dimits transition itself is found to coincide with a tertiary instability threshold, so long as linear effects are included. Through a simple and readily extendable procedure, tracing its origin to St-Onge (J. Plasma Phys., vol. 83, issue 05, 2017, 905830504), the stabilising effect of the typical zonal profile can be approximated, and the accompanying reduced mode estimate is found to be in good agreement with nonlinear simulations.

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Experimental Evidence of Nonlinear Spectral Power Transfer In Zonal Flow Generation

10.1063/1.1593884 ◽

2003 ◽

Author(s):

H. Xia

Keyword(s):

Experimental Evidence ◽

Spectral Power ◽

Zonal Flow ◽

Power Transfer ◽

Flow Generation

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On the robustness of emptying filling boxes to sudden changes in the wind

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.199 ◽

2019 ◽

Vol 868 ◽

Author(s):

John Craske ◽

Graham O. Hughes

Keyword(s):

Thermal Stratification ◽

Temporal Variations ◽

Transient Dynamics ◽

Upper And Lower Bounds ◽

Marginal Stability ◽

Confined Space ◽

Forward Displacement ◽

Previous Formulation ◽

Instantaneous Increase ◽

Good Agreement

We determine the smallest instantaneous increase in the strength of an opposing wind that is necessary to permanently reverse the forward displacement flow that is driven by a two-layer thermal stratification. With an interpretation in terms of the flow’s energetics, the results clarify why the ventilation of a confined space with a stably stratified buoyancy field is less susceptible to being permanently reversed by the wind than the ventilation of a space with a uniform buoyancy field. For large opposing wind strengths we derive analytical upper and lower bounds for the system’s marginal stability, which exhibit a good agreement with the exact solution, even for modest opposing wind strengths. The work extends a previous formulation of the problem (Lishman & Woods, Build. Environ., vol. 44 (4), 2009, pp. 666–673) by accounting for the transient dynamics and energetics associated with the homogenisation of the interior, which prove to play a significant role in buffering temporal variations in the wind.

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Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/3942152 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Keltoum Chahour ◽

Rajae Aboulaich ◽

Abderrahmane Habbal ◽

Nejib Zemzemi ◽

Chérif Abdelkhirane

Keyword(s):

Boundary Conditions ◽

Flow Model ◽

Fluid Model ◽

Invasive Procedure ◽

Navier Stokes ◽

Fractional Flow ◽

Flow Reserve ◽

Arbitrary Position ◽

Model Versus ◽

Good Agreement

Fractional flow reserve (FFR) has proved its efficiency in improving patient diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and use a coupled multidomain method to implement Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the virtual FFR and conduct several numerical experiments. We compare FFR results from the Navier–Stokes model versus generalized flow model and for Windkessel versus traction-free outlet boundary conditions or mixed outlet boundary conditions. We also investigate some sources of uncertainty that the FFR index might encounter during the invasive procedure, in particular, the arbitrary position of the distal sensor. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between the Navier–Stokes model and the non-Newtonian flow model adopted in classifying coronary lesions. Furthermore, we highlight that the lack of standardization while making FFR measurement might be misleading regarding the significance of stenosis.

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Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Processes ◽

10.3390/pr8070810 ◽

2020 ◽

Vol 8 (7) ◽

pp. 810

Author(s):

Jade Gesare Abuga ◽

Tiri Chinyoka

Keyword(s):

Finite Volume ◽

Numerical Algorithm ◽

Numerical Study ◽

Fluid Model ◽

Shear Banding ◽

Numerical Algorithms ◽

Viscoelastic Fluids ◽

Two Fluid Model ◽

Two Fluid ◽

Good Agreement

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

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Characterization of zonal flow generation in weak electrostatic turbulence

Physica Scripta ◽

10.1088/0031-8949/77/05/055502 ◽

2008 ◽

Vol 77 (5) ◽

pp. 055502 ◽

Cited By ~ 4

Author(s):

M Negrea ◽

I Petrisor ◽

B Weyssow

Keyword(s):

Zonal Flow ◽

Flow Generation

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Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

Journal of Plasma Physics ◽

10.1017/s0022377816000921 ◽

2016 ◽

Vol 82 (6) ◽

Cited By ~ 9

Author(s):

E. Tassi ◽

P. L. Sulem ◽

T. Passot

Keyword(s):

Fluid Model ◽

Collisionless Plasma ◽

Low Frequency ◽

Wave Model ◽

Plasma Phys ◽

Alfven Wave ◽

Larmor Radius ◽

Closure Relation ◽

Reduced Models ◽

Finite Larmor Radius

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

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Effects of parallel ion motion on zonal flow generation in ion-temperature-gradient mode turbulence

Physics of Plasmas ◽

10.1063/1.2761861 ◽

2007 ◽

Vol 14 (8) ◽

pp. 082313 ◽

Cited By ~ 4

Author(s):

J. Anderson ◽

J. Li ◽

Y. Kishimoto

Keyword(s):

Temperature Gradient ◽

Zonal Flow ◽

Ion Temperature ◽

Ion Temperature Gradient ◽

Ion Motion ◽

Flow Generation ◽

Gradient Mode

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A pressure tensor description for the time-resonant Weibel instability

Journal of Plasma Physics ◽

10.1017/s0022377816001264 ◽

2017 ◽

Vol 83 (1) ◽

Cited By ~ 2

Author(s):

M. Sarrat ◽

D. Del Sarto ◽

A. Ghizzo

Keyword(s):

Growth Rate ◽

Fluid Model ◽

Plasma Phys ◽

Pressure Tensor ◽

Weibel Instability ◽

Stream Instability

We discuss a fluid model with inclusion of the complete pressure tensor dynamics for the description of Weibel-type instabilities in a counterstreaming beam configuration. Differently from the case recently studied in Sarrat et al. (Europhys. Lett., vol. 115, 2016, 45001), where perturbations perpendicular to the beams were considered, here we focus only on modes propagating along the beams. Such a configuration is responsible for the growth of two kinds of instabilities, the two-stream instability and the Weibel instability, which in this geometry becomes ‘time resonant’, i.e. propagating. This fluid description agrees with the kinetic one and makes it possible e.g. to identify the transition between non-propagating and propagating Weibel modes, already evidenced by Lazar et al. (J. Plasma Phys., vol. 76 (1), 2010, p. 49) as a ‘slope breaking’ of the growth rate, in terms of a merger of two non-propagating Weibel modes.

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