Turbulent energy transfer into zonal flows from the weak to the strong flow shear regime in the stellarator TJ-K

2021 ◽  
Vol 28 (5) ◽  
pp. 052502
Author(s):  
T. Ullmann ◽  
B. Schmid ◽  
P. Manz ◽  
G. E. M. Tovar ◽  
M. Ramisch
Keyword(s):  
Energy Transfer ◽  
Turbulent Energy ◽  
Flow Shear ◽  
Zonal Flows

scholarly journals Frequency-Resolved Nonlinear Turbulent Energy Transfer into Zonal Flows in Strongly HeatedL-Mode Plasmas in the HL-2A Tokamak

2012 ◽  
Vol 108 (24) ◽  
Author(s):  
M. Xu ◽  
G. R. Tynan ◽  
P. H. Diamond ◽  
P. Manz ◽  
C. Holland ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Turbulent Energy ◽  
Zonal Flows

scholarly journals Theory of the tertiary instability and the Dimits shift within a scalar model

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
Hongxuan Zhu ◽  
Yao Zhou ◽  
I. Y. Dodin
Keyword(s):  
Turbulent Transport ◽  
Plasma Phys ◽  
Magnetized Plasma ◽  
Radial Coordinate ◽  
Flow Shear ◽  
Zonal Flows ◽  
Drift Wave ◽  
Zonal Velocity ◽  
Instability Growth ◽  
Traditional Paradigm

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge (J. Plasma Phys., vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

Turbulent energy transfer in bidimensional numerical models of plasma

2021 ◽  
Author(s):  
Rocio Manobanda ◽  
Christian Vasconez ◽  
Denise Perrone ◽  
Raffaele Marino ◽  
Dimitri Laveder ◽  
...  
Keyword(s):  
Solar Wind ◽  
Energy Transfer ◽  
Numerical Models ◽  
Collisionless Plasma ◽  
Space Plasma ◽  
Turbulent Energy ◽  
Turbulent Medium ◽  
Scaling Properties ◽  
Magnetic Diffusivity ◽  
Out Of Plane

<p>Structured, highly variable and virtually collision-free. Space plasma is an unique laboratory for studying the transfer of energy in a highly turbulent environment. This turbulent medium plays an important role in various aspects of the Solar--Wind generation, particles acceleration and heating, and even in the propagation of cosmic rays. Moreover, the Solar Wind continuous expansion develops a strong turbulent character, which evolves towards a state that resembles the well-known hydrodynamic turbulence (Bruno and Carbone). This turbulence is then dissipated from magnetohydrodynamic (MHD) through kinetic scales by different -not yet well understood- mechanisms. In the MHD approach, Kolmogorov-like behaviour is supported by power-law spectra and intermittency measured in observations of magnetic and velocity fluctuations. In this regime, the intermittent cross-scale energy transfer has been extensively described by the Politano--Pouquet (global) law, which is based on conservation laws of the MHD invariants, and was recently expanded to take into account the physics at the bottom of the inertial (or Hall) range, e.g. (Ferrand et al., 2019). Following the 'Turbulence Dissipation Challenge', we study the properties of the turbulent energy transfer using three different bi-dimensional numerical models of space plasma. The models, Hall-MHD (HMHD), Landau Fluid (LF) and Hybrid Vlasov-Maxwell (HVM), were ran in collisionless-plasma conditions, with an out-of-plane ambient magnetic field, and with magnetic diffusivity carefully calibrated in the fluid models. As each model has its own range of validity, it allows us to explore a long-enough range of scales at a period of maximal turbulence activity. Here, we estimate the local and global scaling properties of different energy channels using a, recently introduced, proxy of the local turbulent energy transfer (LET) rate (Sorriso-Valvo et al., 2018). This study provides information on the structure of the energy fluxes that transfers (and dissipates) most of the energy at small scales throughout the turbulent cascade. </p>

scholarly journals Structure function measurements of the intermittent MHD turbulent cascade

1997 ◽  
Vol 4 (3) ◽  
pp. 185-199 ◽  
Author(s):  
T. S. Horbury ◽  
A. Balogh
Keyword(s):  
Energy Transfer ◽  
High Speed ◽  
Solar Wind Plasma ◽  
Turbulent Energy ◽  
Structure Functions ◽  
Order Structure ◽  
Data Sets ◽  
Magnetic Field Data ◽  
Spacecraft Data ◽  
Turbulent Cascade

Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.

scholarly journals How eigenmode self-interaction affects zonal flows and convergence of tokamak core turbulence with toroidal system size

2020 ◽  
Vol 86 (5) ◽  
Author(s):  
Ajay C. J. ◽  
Stephan Brunner ◽  
Ben McMillan ◽  
Justin Ball ◽  
Julien Dominski ◽  
...  
Keyword(s):  
Turbulent Transport ◽  
Zonal Flow ◽  
System Size ◽  
Flow Shear ◽  
Direction Parallel ◽  
Zonal Flows ◽  
Radial Extent ◽  
Modulational Instabilities ◽  
Gyrokinetic Simulations ◽  
The Magnetic Field

Self-interaction is the process by which a microinstability eigenmode that is extended along the direction parallel to the magnetic field interacts non-linearly with itself. This effect is particularly significant in gyrokinetic simulations accounting for kinetic passing electron dynamics and is known to generate stationary $E\times B$ zonal flow shear layers at radial locations near low-order mode rational surfaces (Weikl et al. Phys. Plasmas, vol. 25, 2018, 072305). We find that self-interaction, in fact, plays a very significant role in also generating fluctuating zonal flows, which is critical to regulating turbulent transport throughout the radial extent. Unlike the usual picture of zonal flow drive in which microinstability eigenmodes coherently amplify the flow via modulational instabilities, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. It is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds to an increase in the toroidal system size, leading to a finite system size effect that is distinct from the well-known profile shearing effect.

Helical turbulence and absolute equilibrium

1973 ◽  
Vol 59 (4) ◽  
pp. 745-752 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Energy Transfer ◽  
Isotropic Turbulence ◽  
Negative Temperature ◽  
Inviscid Flow ◽  
Turbulent Energy ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Helical Turbulence ◽  
The Absolute

The interaction of two pure helical (circularly polarized) velocity waves according to the incompressible Navier–Stokes equation produces modulation products of mixed helicity. In general, the interaction of waves of opposite helicity is stronger than that of waves with the same helicity. The inference is that strong net helicity depresses overall turbulent energy transfer. The conservation laws strongly inhibit energy transfer from higher to lower wavenumbers, when the helicity is large. The absolute equilibrium spectra of velocity and helicity for an inviscid flow system truncated at an upper wavenumber k2 are \[ U(k) = 2\alpha/(\alpha^2-\beta^2k^2),\quad Q(k) = 2\beta k^2/(\alpha^2-\beta^2k^2), \] where the velocity variance and helicity/unit volume are ∫U(k)d3k and ∫Q(k)d3k, respectively. The temperature parameters α and β are constrained by α > 0 and |βk2| < α. There are no analogues of the negative-temperature equilibrium states known for two-dimensional inviscid flow. It is argued that the inertial-range energy cascade in isotropic turbulence driven by helical input should not differ asymptotically from that of non-helical turbulence. The absolute equilibrium distributions suggest that, in contrast to the analogous two-dimensional situation, statistically steady helical input at middle wavenumbers should not produce a significant downward cascade of energy to lower wavenumbers.

scholarly journals The role of additive and multiplicative noise in filtering complex dynamical systems

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130096 ◽  
Author(s):  
Georg A. Gottwald ◽  
John Harlim
Keyword(s):  
Energy Transfer ◽  
Dynamical Systems ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Nonlinear Problems ◽  
Forecast Model ◽  
Turbulent Energy ◽  
Test Model ◽  
Model Errors ◽  
Time Data

Covariance inflation is an ad hoc treatment that is widely used in practical real-time data assimilation algorithms to mitigate covariance underestimation owing to model errors, nonlinearity, or/and, in the context of ensemble filters, insufficient ensemble size. In this paper, we systematically derive an effective ‘statistical’ inflation for filtering multi-scale dynamical systems with moderate scale gap, , to the case of no scale gap with , in the presence of model errors through reduced dynamics from rigorous stochastic subgrid-scale parametrizations. We will demonstrate that for linear problems, an effective covariance inflation is achieved by a systematically derived additive noise in the forecast model, producing superior filtering skill. For nonlinear problems, we will study an analytically solvable stochastic test model, mimicking turbulent signals in regimes ranging from a turbulent energy transfer range to a dissipative range to a laminar regime. In this context, we will show that multiplicative noise naturally arises in addition to additive noise in a reduced stochastic forecast model. Subsequently, we will show that a ‘statistical’ inflation factor that involves mean correction in addition to covariance inflation is necessary to achieve accurate filtering in the presence of intermittent instability in both the turbulent energy transfer range and the dissipative range.

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