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Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium.Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012)Proc Natl Acad Sci USA109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and Magnetospheric Multiscale (MMS) spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures, we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.

Using large resolution numerical simulations of gyrokinetic (GK) turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron plasma in a slab equilibrium magnetic geometry. The plasma parameters employed here are relevant to kinetic Alfvén wave turbulence in solar wind conditions. In addition, we use an idealized test representation for the energy transfers between two scales, to aid our understanding of the diagnostics applicable to the nonlinear cascade in an infinite inertial range. For GK turbulence, a detailed analysis of nonlinear energy transfers that account for the separation of energy exchanging scales is performed. Starting from the study of the energy cascade and the scale locality problem, we show that the general nonlocal nature of GK turbulence, captured via locality functions, contains a subset of interactions that are deemed local, are scale invariant (i.e. a sign of asymptotic locality) and possess a locality exponent that can be recovered directly from measurements on the energy cascade. It is the first time that GK turbulence is shown to possess an asymptotic local component, even if the overall locality of interactions is nonlocal. The results presented here and their implications are discussed from the perspective of previous findings reported in the literature and the idea of universality of GK turbulence.

Local gyrokinetic simulations, performed with the GENE code, are used to investigate the interaction between (negative) triangularity $\\delta$ and magnetic shear $s$, in both ion temperature gradient and trapped electron mode dominated plasmas. Magnetic shear turns out to influence in a non-trivial way the effect of negative triangularity. Also, $\\delta <0$ is found to lead to a reduction of fluxes when $s>1$ but not anymore when shear is reduced. In certain parameter regimes, this effect can be inverted, up to obtaining higher fluxes when $\\delta <0$ with respect to its $\\delta >0$ counterpart.

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor $q$, electron beta $\\beta _e$ and normalized electron Debye length $\\lambda _D$, in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport.

In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can be investigated explicitly. This prevents straightforward approaches to important tasks like uncertainty quantification and sensitivity analysis. This challenge can be overcome via our recently developed sensitivity-driven dimension-adaptive sparse grid interpolation strategy. The method exploits, via adaptivity, the structure of the underlying model (such as lower intrinsic dimensionality and anisotropic coupling of the uncertain inputs) to enable efficient and accurate uncertainty quantification and sensitivity analysis at scale. Here, we demonstrate the efficiency of this adaptive approach in the context of fusion research, in a realistic, computationally expensive scenario of turbulent transport in a magnetic confinement tokamak device with eight uncertain parameters, reducing the effort by at least two orders of magnitude. In addition, we show that this refinement method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model. Ionuţ-Gabriel Farcaş, Gabriele Merlo and colleagues developed a framework for uncertainty quantification and sensitivity analysis at scale by focusing on important input parameters. The framework was demonstrated to reduce computational effort and cost compared to standard methods in a turbulent transport simulation in the context of fusion research.

The GENE-3D code, the global stellarator version of the established GENE framework, has been extended to an electromagnetic gyrokinetic code. This paper outlines the basic structure of the algorithm, highlighting the treatment of the electromagnetic terms. The numerical implementation is verified against the radially global GENE code in linear and nonlinear tokamak simulations, recovering excellent agreement between both codes. As a first application to stellarator plasmas, linear and nonlinear global simulations with kinetic electrons of ion temperature gradient (ITG) turbulence in Wendelstein 7-X were performed, showing a decrease of ITG activity through the introduction of electromagnetic effects via a finite plasma-$\\beta$. The upgrade makes it possible to study a large variety of new physical scenarios, including kinetic electron and electromagnetic effects, reducing the gap between gyrokinetic models and physically realistic systems.

In the present paper, we use a coarse-graining approach to investigate the nonlinear redistribution of free energy in both position and scale space for weakly collisional magnetised plasma turbulence. For this purpose, we use high-resolution numerical simulations of gyrokinetic (GK) turbulence that span the proton–electron range of scales, in a straight magnetic guide field geometry. Accounting for the averaged effect of the particles’ fast gyro-motion on the slow plasma fluctuations, the GK approximation captures the dominant energy redistribution mechanisms in strongly magnetised plasma turbulence. Here, the GK system is coarse grained with respect to a cut-off scale, separating in real space the contributions to the nonlinear interactions from the coarse-grid scales and the sub-grid scales (SGS). We concentrate on the analysis of nonlinear SGS effects. Not only does this allow us to investigate the flux of free energy across the scales, but also to now analyse its spatial density. We find that the net value of scale flux is an order of magnitude smaller than both the positive and negative flux density contributions. The dependence of the results on the filter type is also analysed. Moreover, we investigate the advection of energy in position space. This rather novel approach for GK turbulence can help in the development of SGS models that account for advective unstable structures for space and fusion plasmas, and with the analysis of the turbulent transport saturation.

We present a method to estimate the mean and uncertainty of fluctuating quantities, such as spatially averaged density and temperature fluctuations or radial fluxes, from initial value simulations of the Eulerian gyrokinetic code GENE[1, 2]. Since the time series are autocorrelated in time, the data is grouped into batches based on the autocorrelation time and their means form the sample for further statistical treatment, such as calculating the standard error of the mean.Based on this uncertainty estimate we develop a stopping rule for a nonlinear simulation: First, regression tests ensure that it has reached a stationary (quasisteady) state and data before this point is discarded. Then the previously described estimate is calculated. If the estimated relative error is below a prescribed threshold, the simulation is stopped. This scheme is applied to several previously performed GENE simulations ranging from simple benchmarks to modelling of JET and ASDEX discharges. It can be demonstrated that a number of simulations could be around 30% shorter if a maximal statistical relative uncertainty of 5% is desired for all monitored quantities.