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For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.

Near the threshold of grain motion, sediment transport is “on‐off” intermittent, characterized by large but rare bursts separated by long periods of low transport. Without models that can account for the effects of intermittency, measurements of average sediment flux can be in error by up to an order of magnitude. Despite its known presence and impact, it is not clear whether on‐off intermittency arises from the grain activity (the number of moving grains) or grain velocities, which together determine the sediment flux. We use laboratory flume experiments to show that the on‐off intermittency has its origins in the velocity distributions of grains that move by rolling along the bed, whereas grain activity is not on‐off intermittent. Incorporating the types of intermittency we identify into stochastic models of sediment transport could yield improved predictions of sediment flux, including physically based estimates of the uncertainty in time‐averaged sediment flux. Plain Language Summary Sediment, such as sand and gravel, is transported across the surface of the Earth and other planets by wind and water. Predicting the amount of sediment that can be transported given a certain flow rate is crucial for predicting how a landscape will change over time. For low flow rates, little to no grain motion occurs. Just beyond the flow rate required for motion, sediment transport occurs mostly in rare bursts. This so‐called “on‐off” intermittency creates difficulties when trying to measure the average transport rate, which must be done over longer time periods as the bursts become larger but less frequent. While on‐off intermittency has been identified in previous studies of sediment transport, there is currently no understanding of its physical origin. We use a series of experiments in a small laboratory river to show that the on‐off intermittency is due to large fluctuations in the speed of the grains rolling on the bed, and that the sediment transport becomes less bursty as more grains are lifted off the river bed and into the fluid. Our results will pave the way for better measurements and predictions of sediment transport in rivers. Key Points We use grain tracking data from laboratory experiments to separately study the statistics of grain velocities and grain activity We show that on‐off intermittency has its origins in the velocity distributions of grains, not in the grain activity On‐off intermittency comes from grains rolling on the bed, and disappears as more and more grains are lifted into the bulk of the flow

Driven by global concerns about the climate and the environment, the world is opting for renewable energy sources (RESs), such as wind and solar. However, RESs suffer from the discredit of intermittency, for which energy storage systems (ESSs) are gaining popularity worldwide. Surplus energy obtained from RESs can be stored in several ways, and later utilized during periods of intermittencies or shortages. The idea of storing excess energy is not new, and numerous researches have been conducted to adorn this idea with innovations and improvements. This review is a humble attempt to assemble all the available knowledge on ESSs to benefit novice researchers in this field. This paper covers all core concepts of ESSs, including its evolution, elaborate classification, their comparison, the current scenario, applications, business models, environmental impacts, policies, barriers and probable solutions, and future prospects. This elaborate discussion on energy storage systems will act as a reliable reference and a framework for future developments in this field. Any future progress regarding ESSs will find this paper a helpful document wherein all necessary information has been assembled.

Deviating from homogeneous isotropic turbulence, we analyze a large amount of experimental data with respect to the dimensionless dissipation constant, the intermittency parameter, and the multiplicative noise in a corresponding stochastic process description of the cascade. We find that all three parameters are strongly related to each other. Although these parameters contain quite different information about turbulence, it is sufficient to know one to estimate all other parameters. This suggests that our results imply a new generalization.

In studies of turbulence, there has been extensive use of physical quantities such as {\\it energy transfers} and {\\it structure functions}. We examine whether these quantities can be useful in understanding problems of domain growth or coarsening, as modeled by the {\\it time-dependent Ginzburg-Landau} (TDGL) equation and the {\\it Cahn-Hilliard} (CH) equation. This paper has two major themes. First, we review our recent papers on energy transfers in domain growth. Second, we study structure functions and intermittency for coarsening systems. As a consequence of sharp interfaces, the structure functions scale as \\(S_q \\sim r^{\\zeta_q}\\), where \\(r\\) is the distance between two points. For the TDGL and CH models, \\(\\zeta_q = 1\\), indicating {\\it anomalous scaling}

This review of scaling theories of magnetohydrodynamic (MHD) turbulence aims to put the developments of the last few years in the context of the canonical time line (from Kolmogorov to Iroshnikov–Kraichnan to Goldreich–Sridhar to Boldyrev). It is argued that Beresnyak's (valid) objection that Boldyrev's alignment theory, at least in its original form, violates the Reduced-MHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, a version of which is recovered in this interpretation, and the concept of dynamic alignment (equivalently, local 3D anisotropy) are thus an example of a physical theory of intermittency in a turbulent system. The emergence of aligned structures naturally brings into play reconnection physics and thus the theory of MHD turbulence becomes intertwined with the physics of tearing, current-sheet disruption and plasmoid formation. Recent work on these subjects by Loureiro, Mallet et al. is reviewed and it is argued that we may, as a result, finally have a reasonably complete picture of the MHD turbulent cascade (forced, balanced, and in the presence of a strong mean field) all the way to the dissipation scale. This picture appears to reconcile Beresnyak's advocacy of the Kolmogorov scaling of the dissipation cutoff (as $\\mathrm {Re}^{3/4}$) with Boldyrev's aligned cascade. It turns out also that these ideas open the door to some progress in understanding MHD turbulence without a mean field – MHD dynamo – whose saturated state is argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart (this is a new result). On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require some adjustment – and a new scheme for such an adjustment is proposed – to take account of the determining part that a spontaneously emergent 2D condensate plays in mediating the Alfvén-wave cascade from a weakly interacting state to a strongly turbulent (critically balanced) one. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed: imbalanced turbulence (for which a new, tentative theory is proposed), residual energy, MHD turbulence at subviscous scales, and decaying MHD turbulence (where there has been dramatic progress recently, and reconnection again turned out to feature prominently). Finally, it is argued that the natural direction of research is now away from the fluid MHD theory and into kinetic territory – and then, possibly, back again. The review lays no claim to objectivity or completeness, focusing on topics and views that the author finds most appealing at the present moment.

Randomness and intermittency are crucial challenges in photovoltaic (PV) power prediction. Most studies concentrate on addressing the randomness of PV power, and tend to overlook the intermittency that leads to sample imbalance, which negatively affects prediction accuracy. To address the sample imbalance, a novel approach called segment imbalance regression (SIR) is proposed. The SIR method proactively exploits the inherent imbalanced nature of samples by investigating the interactions among neighbouring samples, which leads to dynamical assigning weights. Through focused training and segmental prediction, SIR selectively retains the outside information while focusing segment inside, which enhances the gradient descent process and ultimately leads to improved training performance. With crisscross optimization (CSO), SIR demonstrates its performance sufficiently with an average RMSE reduction of 21.17% and 40.76% in the multi-step prediction and day-ahead prediction cases, respectively.

The initiation threshold of sediment motion, a key component in quantifying sediment transport, has potential link to intermittent turbulence bursts. Here, we elaborated in situ experiments on coastal sea bottom covered with cohesive sediments, to obtain intermittency parameters. The variable “waiting time” between turbulence bursts was utilized to capture the occurrence of sediment initiation events in natural waters. A relationship between waiting time and shear stress reveals the different intermittency features of sediment flux time series before and after reaching the threshold, which can be used to determine the initiation threshold of sediment motion. Multi‐site results demonstrate the limitations of traditional empirical formulae for fine‐grained sediments, where cohesiveness becomes more pronounced as grain size decreases and the deviation can reach 600%. The empirical formula was modified using grain size, and the modified calculations were in good agreement with observed values, which will greatly assist in sediment transport and geomorphology model predictions. Plain Language Summary As an on‐off switch for sediment transport, sediment initiation determines the redistribution of matter and the geomorphological evolution. Researchers have confirmed a link between intermittency and sediment initiation, yet how to parameterize and utilize has not been studied in depth. Here, the ability to capture sediment initiation events using intermittency metrics is verified for the first time with numerous in situ observations of high‐resolution velocity and sediment concentration data. Furthermore, a new procedure of utilizing field data to determine the initiation threshold was proposed by using the distribution relationship between the bottom shear stress and intermittency metric. Increasing differences between the newly determined threshold and empirical formula results correlate with the decrease in grain size. Such knowledge greatly helps improve the accuracy of threshold determination which in turn contributes to the accurate prediction of sediment transport models and thus engineering applications. Key Points Field‐measured intermittency indicators effectively identify sediment motion initiation, aligning with laboratory findings on shear stress Leveraging the relationship between intermittency indicator and shear stress enables precise determination of sediment initiation threshold We propose a modified formula incorporating grain size to more accurately calculate the critical shear stress of fine‐grained sediments

We expose a hidden scaling symmetry of the Navier–Stokes equations in the limit of vanishing viscosity, which stems from dynamical space–time rescaling around suitably defined Lagrangian scaling centres. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.

We have performed direct numerical simulations of homogeneous and isotropic turbulence in a periodic box with 8,192³ grid points. These are the largest simulations performed, to date, aimed at improving our understanding of turbulence small-scale structure. We present some basic statistical results and focus on “extreme” events (whose magnitudes are several tens of thousands the mean value). The structure of these extreme events is quite different from that of moderately large events (of the order of 10 times the mean value). In particular, intense vorticity occurs primarily in the form of tubes for moderately large events whereas it is much more “chunky” for extreme events (though probably overlaid on the traditional vortex tubes). We track the temporal evolution of extreme events and find that they are generally shortlived. Extreme magnitudes of energy dissipation rate and enstrophy occur simultaneously in space and remain nearly colocated during their evolution.