Vlasov simulations of Kinetic Alfv\'en Waves at proton kinetic scales

Kinetic Alfv\'en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length $d_p$ and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfv\'en waves at proton kinetic scales, in typical conditions of the solar wind environment. In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to $d_p$ and proton plasma beta $\beta$ of order unity the kinetic Alfv\'en waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects

The hydrodynamic genesis of linear karren patterns

In karst and alpine areas, the interactions between water and rocks give rise to a large variety of marvellous patterns. In this work, we provide a hydrodynamic model for the formation of dissolutional patterns made of parallel longitudinal channels, commonly referred to as linear karren forms. The model addresses a laminar film of water flowing on a rock that is dissolving. The results show that a transverse instability of the water–rock system leads to a longitudinal channelization responsible for the pattern formation. The instability arises because of a positive feedback within the channels between the higher water flow and the enhanced chemical dissolution. The spatial scales predicted by the linear stability analysis span different orders of magnitude depending on the Reynolds number. This may explain why similar patterns of different sizes are observed on natural rocks. Results also show that the rock solubility affects just the temporal scale of the instability and the rock inclination plays a minor role in the pattern formation. It is eventually discussed how rain is not strictly necessary for the appearance of linear karren patterns, but it may affect some of their features

Noise-driven cooperative dynamics between vegetation and topography in riparian zones

Riparian ecosystems exhibit complex biotic and abiotic dynamics, where the triad vegetation-sediments-stream determines the ecogeomorphological features of the river landscape. Random fluctuations of the water stage are a key trait of this triad, and a number of behaviors of the fluvial environment can be understood only taking into consideration the role of noise. In order to elucidate how randomness shape riparian transects, a stochastic model that takes into account the main links between vegetation, sediments, and the stream is adopted, emphasizing the capability of vegetation to alter the plot topography. A minimalistic approach is pursued, and the probability density function of vegetation biomass is analytically evaluated in any transect plot. This probability density function strongly depends on the vegetation-topography feedback. We demonstrate how the vegetation-induced modifications of the bed topography create more suitable conditions for the survival of vegetation in a stochastically dominated environment

Probabilistic prediction of Dst storms one-day-ahead using Full-Disk SoHO Images

We present a new model for the probability that the Disturbance storm time (Dst) index exceeds -100 nT, with a lead time between 1 and 3 days. $Dst$ provides essential information about the strength of the ring current around the Earth caused by the protons and electrons from the solar wind, and it is routinely used as a proxy for geomagnetic storms. The model is developed using an ensemble of Convolutional Neural Networks (CNNs) that are trained using SoHO images (MDI, EIT and LASCO). The relationship between the SoHO images and the solar wind has been investigated by many researchers, but these studies have not explicitly considered using SoHO images to predict the $Dst$ index. This work presents a novel methodology to train the individual models and to learn the optimal ensemble weights iteratively, by using a customized class-balanced mean square error (CB-MSE) loss function tied to a least-squares (LS) based ensemble. The proposed model can predict the probability that Dst<-100 nT 24 hours ahead with a True Skill Statistic (TSS) of 0.62 and Matthews Correlation Coefficient (MCC) of 0.37. The weighted TSS and MCC from Guastavino et al. (2021) is 0.68 and 0.47, respectively. An additional validation during non-Earth-directed CME periods is also conducted which yields a good TSS and MCC score.Comment: accepted by journal <Space Weather

Interplay among unstable modes in films over permeable walls

The stability of open-channel flows (or film flows) has been extensively investigated for the case of impermeable smooth walls. In contrast, despite its relevance in many geophysical and industrial flows, the case that considers a permeable rather than an impermeable wall is almost unexplored. In the present work, a linear stability analysis of a film falling over a permeable and inclined wall is developed and discussed. The focus is on the mutual interaction between three modes of instability, namely, the well-known free-surface and hydrodynamic (i.e. shear) modes, which are commonly observed in open-channel flows over impermeable walls, plus a new one associated with the flow within the permeable wall (i.e. the porous mode). The flow in this porous region is modelled by the volume-averaged Navier-Stokes equations and, at the wall interface, the surface and subsurface flow are coupled through a stress-jump condition, which allows one to obtain a continuous velocity profile throughout the whole flow domain. The generalized eigenvalue problem is then solved via a novel spectral Galerkin method, and the whole spectrum of eigenvalues is presented and physically interpreted. The results show that, in order to perform an analysis with a full coupling between surface and subsurface flow, the convective terms in the volume-averaged equations have to be retained. In previous studies, this aspect has never been considered. For each kind of instability, the critical Reynolds number (${\mathit{Re}}_{c}$) is reported for a wide range of bed slopes ($\theta$) and permeabilities ($\sigma$). The results show that the free-surface mode follows the behaviour that was theoretically predicted by Benjamin and Yih for impermeable walls and is independent of wall permeability. In contrast, the shear mode shows a high dependence on $\sigma$: at $\sigma = 0$ the behaviour of ${\mathit{Re}}_{c} (\theta )$ recovers the well-known non-monotonic behaviour of the impermeable-wall case, with a minimum at \theta \sim 0. 05\textdegree . However, with an increase in wall permeability, ${\mathit{Re}}_{c}$ gradually decreases and eventually recovers a monotonic decreasing behaviour. At high values of $\sigma$, the porous mode of instability also occurs. A physical interpretation of the results is presented on the basis of the interplay between the free-surface-induced perturbation of pressure, the increment of straining due to shear with the increase in slope, and the shear stress condition at the free surface. Finally, the paper investigates the extent to which Squire's theorem is applicable to the problem presented herei

Adaptive selection of sampling points for uncertainty quantification

We present a simple and robust strategy for the selection of sampling points in Uncertainty Quantification. The goal is to achieve the fastest possible convergence in the cumulative distribution function of a stochastic output of interest. We assume that the output of interest is the outcome of a computationally expensive nonlinear mapping of an input random variable, whose probability density function is known. We use a radial function basis to construct an accurate interpolant of the mapping. This strategy enables adding new sampling points one at a time, adaptively. This takes into full account the previous evaluations of the target nonlinear function. We present comparisons with a stochastic collocation method based on the Clenshaw-Curtis quadrature rule, and with an adaptive method based on hierarchical surplus, showing that the new method often results in a large computational saving.Comment: 22 pages, 15 figures; to appear in Int. J. Uncertainty Quantificatio

Hierarchy of models for meandering rivers and related morphodynamic processes

We review the importance of the physical mechanisms involved in river meandering by comparing some existing linear models and extensions thereof. Such models are hierarchically derived from a common and general mathematical framework and then analyzed with a detailed discussion of the physical processes and relevant hypotheses that are involved. Experiments and field data are also used to discuss the related morphodynamic processes. The analysis of the models shows the importance of the closure of secondary currents especially in the modeling of eddy viscosity. This aspect confirms the usefulness of using simplified models for some practical applications, provided the secondary currents are modeled in detail. On the other hand, the free response of the sediments, the phase lag of secondary currents, and the momentum redistribution due to the coupling between the main and the transverse flow are shown to be less relevant. Hence the second-order models, which neglect the effect of superelevation induced by the topography-driven lateral flow on the longitudinal flow, can reasonably be considered a good approximation for both predictive analysis and the computation of the resonant conditions. Finally, the analysis of higher harmonics suggests that the multilobed pattern can intrinsically be present in both second- and fourth-order models

RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE

Turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two dimensional, particle-in-cell (PIC) plasma simulations with realistic electron-proton mass ratio and a guide field out of the simulation plane. A fluctuation power spectrum with approximately power law form is created down to scales of order the electron gyroradius. In the dynamic magnetic field topology, which gradually relaxes in complexity, we identify the signatures of collisionless reconnection at sites of X-point field geometry. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with a strong parallel temperature anisotropy. In a three-dimensional system, supporting the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations.Comment: 27 pages, 14 figures. Accepted for publication in ApJ, Jan 3, 201

A gray-box model for a probabilistic estimate of regional ground magnetic perturbations: Enhancing the NOAA operational Geospace model with machine learning

We present a novel algorithm that predicts the probability that the time derivative of the horizontal component of the ground magnetic field $dB/dt$ exceeds a specified threshold at a given location. This quantity provides important information that is physically relevant to Geomagnetically Induced Currents (GIC), which are electric currents { associated to} sudden changes in the Earth's magnetic field due to Space Weather events. The model follows a 'gray-box' approach by combining the output of a physics-based model with machine learning. Specifically, we combine the University of Michigan's Geospace model that is operational at the NOAA Space Weather Prediction Center, with a boosted ensemble of classification trees. We discuss the problem of re-calibrating the output of the decision tree to obtain reliable probabilities. The performance of the model is assessed by typical metrics for probabilistic forecasts: Probability of Detection and False Detection, True Skill Statistic, Heidke Skill Score, and Receiver Operating Characteristic curve. We show that the ML enhanced algorithm consistently improves all the metrics considered.Comment: under revie

Hybrid solar-biomass combined Brayton/organic Rankine-cycle plants integrated with thermal storage: Techno-economic feasibility in select Mediterranean areas

This paper presents a thermodynamic analysis and techno-economic assessment of a novel hybrid solar-biomass power-generation system configuration composed of an externally fired gas-turbine (EFGT) fuelled by biomass (wood chips) and a bottoming organic Rankine cycle (ORC) plant. The main novelty is related to the heat recovery from the exhaust gases of the EFGT via thermal energy storage (TES), and integration of heat from a parabolic-trough collectors (PTCs) field with molten salts as a heat-transfer fluid (HTF). The presence of a TES between the topping and bottoming cycles facilitates the flexible operation of the system, allows the system to compensate for solar energy input fluctuations, and increases capacity factor and dispatchability. A TES with two molten salt tanks (one cold at 200 °C and one hot at 370 °C) is chosen. The selected bottoming ORC is a superheated recuperative cycle suitable for heat conversion in the operating temperature range of the TES. The whole system is modelled by means of a Python-based software code, and three locations in the Mediterranean area are assumed in order to perform energy-yield analyses: Marseille in France, Priolo Gargallo in Italy and Rabat in Morocco. In each case, the thermal storage that minimizes the levelized cost of energy (LCE) is selected on the basis of the estimated solar radiation and CSP size. The results of the thermodynamic simulations, capital and operational costs assessments and subsidies (feed-in tariffs for biomass and solar electricity available in the Italian framework), allow estimating the global energy conversion efficiency and the investment profitability in the three locations. Sensitivity analyses of the biomass costs, size of PTCs, feed-in tariff and share of cogenerated heat delivered to the load are also performed. The results show that the high investment costs of the CSP section in the proposed size range and hybridization configuration allow investment profitability only in the presence of a dedicated subsidy framework such as the one available in the Italian energy market. In particular, the LCE of the proposed system is around 140 Eur/MWh (with the option to discharge the cogenerated heat) and the IRR is around 15%, based on the Italian electricity subsidy tariffs. The recovery of otherwise discharged heat to match thermal energy demand can significantly increase the investment profitability and compensate the high investment costs of the proposed technology