Suppression of turbulence by self-generated and imposed mean flows

Stochastic Dynamics of Fusion Low-to-High Confinement Mode (L-H) Transition: Correlation and Causal Analyses Using Information Geometry

We investigate the stochastic dynamics of the prey-predator model of the Low-to-High confinement mode (L-H) transition in magnetically confined fusion plasmas. By considering stochastic noise in the turbulence and zonal flows as well as constant and time-varying input power Q, we perform multiple stochastic simulations of over a million trajectories using GPU computing. Due to stochastic noise, some trajectories undergo the L-H transition while others do not, leading to a mixture of H-mode and dithering at a given time and/or input power. One of the consequences of this is that H-mode characteristics appear at a smaller input power QQc as a second peak. The coexisting H-mode and dithering near Q=Qc leads to a prominent bimodal PDF with a gradual L-H transition rather than a sudden transition at Q=Qc and uncertainty in the input power. Also, a time-dependent input power leads to increased variability (dispersion) in stochastic trajectories and a more prominent bimodal PDF. We provide an interpretation of the results using information geometry to elucidate self-regulation between zonal flows, turbulence, and information causality rate to unravel causal relations involved in the L-H transition.

A stochastic model of edge-localized modes in magnetically confined plasmas

Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated with instabilities in the low-to-high confinement transition and the H-mode. Specifically, we present a stochastic Langevin model of edge-localized modes (ELMs) by including stochastic noise terms in a previous ODE ELM model. We calculate exact time-dependent PDFs by numerically solving the Fokker-Planck equation and characterize time-varying statistical properties of ELMs for different energy fluxes and noise amplitudes. The stochastic noise is shown to introduce phase-mixing and plays a significant role in mitigating extreme bursts of large ELMs. Furthermore, based on time-dependent PDFs, we provide a path-dependent information geometric theory of the ELM dynamics and demonstrate its utility in capturing self-regulatory relaxation oscillations, bursts and a sudden change in the system. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Turbulence and jet-driven zonal flows: Secondary circulation in rotating fluids due to asymmetric forcing

We report on experiments and modeling on a rotating confined liquid that is forced by circumferential jets coaxial with the rotation axis, wherein system-scale secondary flows are observed to emerge. The jets are evenly divided in number between inlets and outlets and have zero net mass transport. For low forcing strengths the sign of this flow depends on the sign of a sloped end cap, which simulates a planetary β plane. For increased forcing strengths the secondary flow direction is insensitive to the slope sign, and instead appears to be dominated by an asymmetry in the forcing mechanism, namely, the difference in radial divergence between the inlet and outlet jet profiles. This asymmetry yields a net radial velocity that is affected by the Coriolis force, inducing secondary zonal flow.

Interaction between mean flow and turbulence in two dimensions

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.

Experimental confirmation of self-regulating turbulence paradigm in two-dimensional spectral condensation

Turbulent transport in magnetic fusion plasmas can be significantly suppressed by Reynolds-stress-induced zonal flows, allowing effective plasma confinement. We present experimental evidence of spatiotemporal correlation between small-scale turbulence-induced Reynolds stress and large-scale zonal flow production in the E×B driven hydrodynamic spectral condensation. We show that Reynolds stress is generated effectively by anisotropic vorticity structures possessing collective tilt angle. The maximum amplitude of the tilt, the Reynolds stress, and the mean zonal flow production coincide with the transition time of the velocity field, indicating a key role of turbulence-induced Reynolds stress in the condensation of the flow. The analysis of the energy transfer between turbulence and zonal flow shows coherent oscillations with π/2 phase delay, thus indicating a predator-prey-like interaction between zonal flow and turbulence.

Inverse energy cascade and turbulent transport in a quasi-two-dimensional magnetized electrolyte system: an experimental study

We present an experimental study of the inverse energy cascade, spectral condensation, and turbulent particle transport in an electromagnetically driven thin layer of NaCl electrolyte. The presence of the bottom friction provides an energy sink at large scales for the turbulent flow. This energy sink crucially contributes to the balance of the forcing and dissipation which makes the inverse cascade steady. The present work provides an estimation of the linear dissipation rate on an experimental basis. We also show how the dissipation rate affects the characteristic features of the velocity spectrum and the dynamics of the spectral condensation. A quantitative study of the turbulent diffusion shows a significant decrease of the radial transport during the spectral condensation process.

Three-dimensional flow in electromagnetically driven shallow two-layer fluids

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the existence and evolution of complex three-dimensional (3D) flow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer fluid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. Remarkably, the experimental results, supported by the numerical simulations, show to a large extent the same 3D structures and evolution as in the single-layer case. The numerical simulations indicate that the so-called frontal circulation in the two-layer fluid is due to deformations of the internal interface. The 3D flow structures will also affect the distribution of massless passive particles released at the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity field is not divergence-free. This is in contrast with pure two-dimensional incompressible flows where the divergence of the velocity field is zero by definition.

Toroidal rotation driven by the polarization drift

Starting from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers a novel mechanism by which microturbulence may drive intrinsic rotation. This mechanism, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the polarization drift. The derivation and physical discussion of this mechanism will be pursued throughout this Letter.

Kinematic alpha effect in the presence of a large-scale motion

We investigate how the addition of a large-scale steady motion, either shear or uniform flow, modifies the magnetic transport properties of a family of chaotic velocity fields with different correlation times. We compute numerically the kinematic alpha effect that those flows give rise to and show that it is reduced by the presence of a large-scale motion parallel to the large-scale magnetic field, except under certain conditions when it can be slightly enhanced via resonances. The alpha effect is shown to depend on the nature of the large-scale motion and on the temporal characteristics of the chaotic flow. These results highlight the strong influence that a shear or a uniform flow can have on the turbulent transport of magnetic fields.

Generic mechanism of microturbulence suppression by vortex flows

The interaction between two-dimensional vortex flows and microturbulence is studied numerically using gyrofluid simulations. It is shown that, qualitatively different from usual mean flows, vortex flows can dramatically suppress microturbulence even with weak flow shear. A generic suppression mechanism is identified as the multiplied effect of both radial and poloidal mode couplings, which induce the formation of a new global mode. Furthermore, an oscillatory zonal flow is found to form through interaction between the vortex flows and microturbulence.

Rapid generation of angular momentum in bounded magnetized plasma

Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in nonaxisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a larger time scale, the generation of a magnetic angular momentum, or angular field, is observed. For axisymmetric geometries, the generation of angular momentum is absent; nevertheless, a weak magnetic field can be observed. The derived evolution equations for both the angular momentum and angular field yield possible explanations for the observed behavior.

Turbulence-condensate interaction in two dimensions

We present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It is shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in the inverse cascade. This observation may help resolve a controversy on the energy flux in mesoscale atmospheric turbulence (10-500 km): to recover a correct energy flux from the third velocity moment one needs first to subtract the coherent flow. We find that the condensate also increases the velocity flatness.

Simultaneous numerical simulation of direct and inverse cascades in wave turbulence

The results of the direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time, the simultaneous formation of both direct and inverse cascades has been observed in the framework of the primordial dynamical equations. At the same time, a strong long wave background has been developed. It has been shown that the Kolmogorov spectra obtained are very sensitive to the presence of this condensate. Such a situation has to be typical for experimental wave tanks, flumes, and small lakes.