arXiv subjects

Michele Buzzicotti

Publications and source records attributed to Michele Buzzicotti.

At least 37 records · Page 2Linked to original sources

arXiv2023

Global Cascade of Kinetic Energy in the Ocean and the Atmospheric Imprint

We present the first estimate for the ocean's global scale-transfer of kinetic energy (KE), across scales from 10~km to 40000~km. We show the existence of oceanic KE transfer between gyre-scales and mesoscales induced by the atmosphere's Hadley, Ferrel, and polar cells, and intense downscale KE transfer associated with the Inter-Tropical Convergence Zone. We report peak upscale transfer of 300 GigaWatts across mesoscales of 120~km in size, roughly 1/3rd the energy input by winds into the oceanic general circulation. This "cascade" penetrates almost the entire water column, with nearly three quarters of it occurring south of 15$^\circ$S. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag-time of $\mathbf{\approx27~}$days per octave of length-scales such that transfer across 50~km peaks in spring while transfer across 500~km peaks in summer. KE content of those mesoscales follows the same self-similar cycle but peaks $\mathbf{\approx40~}$days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale 4$\times$ larger.

physics.ao-ph↗

arXiv2023

Multi-scale data reconstruction of turbulent rotating flows with Gappy POD, Extended POD and Generative Adversarial Networks

Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades, which lead to non-Gaussian statistics at both large and small scales. Data assimilation also serves as a tool to rank physical features within turbulence, by evaluating the performance of reconstruction in terms of the quality and quantity of the information used. Additionally, benchmarking various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity, and explicability. In this study, we use linear and non-linear tools based on the Proper Orthogonal Decomposition (POD) and Generative Adversarial Network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the non-linear GAN does not outperform one of the linear POD techniques. On the other hand, supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training. Robustness against the measurement noise is also discussed.

physics.flu-dyn↗

arXiv2023

Generative Adversarial Networks to infer velocity components in rotating turbulent flows

Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of the linear Extended Proper Orthogonal Decomposition (EPOD) method, a non-linear Convolutional Neural Network (CNN) and a Generative Adversarial Network (GAN). We attack the important task of inferring one velocity component out of the measurement of a second one, and two cases are studied: (I) both components lay in the plane orthogonal to the rotation axis and (II) one of the two is parallel to the rotation axis. We show that EPOD method works well only for the former case where both components are strongly correlated, while CNN and GAN always outperform EPOD both concerning point-wise and statistical reconstructions. For case (II), when the input and output data are weakly correlated, all methods fail to reconstruct faithfully the point-wise information. In this case, only GAN is able to reconstruct the field in a statistical sense. The analysis is performed using both standard validation tools based on $L_2$ spatial distance between the prediction and the ground truth and more sophisticated multi-scale analysis using wavelet decomposition. Statistical validation is based on standard Jensen-Shannon divergence between the probability density functions, spectral properties and multi-scale flatness.

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arXiv2023

Spatio-temporal coarse-graining decomposition of the global ocean geostrophic kinetic energy

We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022) using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales ($>1000~$km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100-500~km) have a root-mean-square (rms) velocity of $\sim15~$cm/s, which increases to $\sim30$-40~cm/s locally in the Gulf Stream and Kuroshio and to $\sim16$-28~cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that $\approx25$-50\% of total geostrophic energy is at scales smaller than 100~km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean component show that most of its energy (up to $70\%$) resides in stationary mesoscales ($<500~$km), highlighting the preponderance of `standing' small-scale structures in the global ocean. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at $\approx200$ km and $\approx2$-3~weeks.

physics.ao-ph↗

arXiv2023

Reconstructing Rayleigh-Benard flows out of temperature-only measurements using Physics-Informed Neural Networks

We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Benard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging and are able to achieve satisfactory reconstruction of the velocity fields only when data for temperature is provided with high spatial and temporal density. When data becomes sparse, the PINNs performance worsens, not only in a point-to-point error sense but also, and contrary to nudging, in a statistical sense, as can be seen in the probability density functions and energy spectra.

physics.flu-dyn↗

arXiv2022

Classifying Turbulent Environments via Machine Learning

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in different turbulent backgrounds, to predict the probability of rare events and/or to infer physical parameters labelling different turbulent set-ups. To achieve such goal one can use different tools depending on the system's knowledge and on the quality and quantity of the accessible data. In this context, we assume to work in a model-free setup completely blind to all dynamical laws, but with a large quantity of (good quality) data for training. As a prototype of complex flows with different attractors, and different multi-scale statistical properties we selected 10 turbulent 'ensembles' by changing the rotation frequency of the frame of reference of the 3d domain and we suppose to have access to a set of partial observations limited to the instantaneous kinetic energy distribution in a 2d plane, as it is often the case in geophysics and astrophysics. We compare results obtained by a Machine Learning (ML) approach consisting of a state-of-the-art Deep Convolutional Neural Network (DCNN) against Bayesian inference which exploits the information on velocity and enstrophy moments. First, we discuss the supremacy of the ML approach, presenting also results at changing the number of training data and of the hyper-parameters. Second, we present an ablation study on the input data aimed to perform a ranking on the importance of the flow features used by the DCNN, helping to identify the main physical contents used by the classifier. Finally, we discuss the main limitations of such data-driven methods and potential interesting applications.

physics.flu-dyn↗

arXiv2022

Global Energy Spectrum of the General Oceanic Circulation

Since the advent of satellite altimetry, our perception of the oceanic circulation has brought into focus the pervasiveness of mesoscale eddies that have typical scales of tens to hundreds of kilometers [5], are the ocean's analogue of weather systems, and are often thought of as the peak of the ocean's kinetic energy (KE) wavenumber spectrum [7, 19, 23]. Yet, our understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small representative regions (e.g. [16, 14, 4]), typically a few hundred kilometers in size, that cannot capture the vast dynamic range at planetary scales. Here, we present the first truly global wavenumber spectrum of the oceanic circulation from satellite data and high-resolution re-analysis data, using a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three orders of magnitude in length-scale reveal the Antarctic Circumpolar Current (ACC) as the spectral peak of the global extra-tropical ocean, at $\approx 10 \times 10^3~$km. We also find a previously unobserved power-law scaling over scales larger than $10^3~$km. A smaller spectral peak exists at $\approx 300~$km associated with the mesoscales, which, due to their wider spread in wavenumber space, account for more than $50\%$ of the resolved surface KE globally. Length-scales that are twice as large (up to $10^3$~km) exhibit a characteristic lag time of $\approx40~$days in their seasonal cycle, such that in both hemispheres KE at $100~$km peaks in late spring while KE at $10^3~$km peaks in late summer. The spectrum presented here affords us a new window for understanding the multiscale general oceanic circulation within Earth's climate system, including the largest planetary scales.

physics.ao-ph↗

arXiv2021

Inertial range statistics of the Entropic Lattice Boltzmann in 3D turbulence

We present a quantitative analysis of the inertial range statistics produced by Entropic Lattice Boltzmann Method (ELBM) in the context of 3d homogeneous and isotropic turbulence. ELBM is a promising mesoscopic model particularly interesting for the study of fully developed turbulent flows because of its intrinsic scalability and its unconditional stability. In the hydrodynamic limit, the ELBM is equivalent to the Navier-Stokes equations with an extra eddy viscosity term [1]. From this macroscopic formulation, we have derived a new hydrodynamical model that can be implemented as a Large-Eddy Simulation (LES) closure. This model is not positive definite, hence, able to reproduce backscatter events of energy transferred from the subgrid to the resolved scales. A statistical comparison of both mesoscopic and macroscopic entropic models based on the ELBM approach is presented and validated against fully resolved Direct Numerical Simulations (DNS). Besides, we provide a second comparison of the ELBM with respect to the well known Smagorinsky closure. We found that ELBM is able to extend the energy spectrum scaling range preserving at the same time the simulation stability. Concerning the statistics of higher order, inertial range observables, ELBM accuracy is shown to be comparable with other approaches such as Smagorinsky model.

physics.flu-dyn↗

arXiv2021

Optimal control of point-to-point navigation in turbulent time-dependent flows using Reinforcement Learning

We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal Navigation (ON) control with stochastic policies obtained by Reinforcement Learning (RL) algorithms. We show that Actor-Critic RL algorithms are able to find quasi-optimal solutions in the presence of either time-independent or chaotically evolving flow configurations. For our application, ON solutions develop unstable behavior within the typical duration of the navigation process, and are therefore not useful in practice. We first explore navigation of turbulent flow using a constant propulsion speed. Based on a discretized phase-space, the propulsion direction is adjusted with the aim to minimize the time spent to reach the target. Further, we explore a case where additional control is obtained by allowing the engine to power off. Exploiting advection of the underlying flow, allows the target to be reached with less energy consumption. In this case, we optimize a linear combination between the total navigation time and the total time the engine is switched off. Our approach can be generalized to other setups, for example, navigation under imperfect environmental forecast or with different models for the moving vessel.

eess.SY↗

arXiv2019

Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning

To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip velocity with fixed intensity, Vs , but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasi-optimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process, and are therefore not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when V s is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.

nlin.CD↗

arXiv2019

Self-similar Subgrid-scale Models for Inertial Range Turbulence and Accurate Measurements of Intermittency

A class of spectral subgrid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of subgrid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale extension where anomalous exponents are measured by roughly one order of magnitude, when compared to direct numerical simulations or to other popular subgrid closures at the same resolution. We found a first indication that intermittency for high order moments is not captured by many of the popular phenomenological models developed so far.

physics.flu-dyn↗

arXiv2019

The statistical properties of turbulence in the presence of a smart small-scale control

By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a non-linear extra viscosity acting preferentially on high vorticity regions. We show that the presence of such smart small-scale drag can strongly reduce intermittency and non-Gaussian fluctuations. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in turbulence as well as on the impact of (pseudo)coherent structures on the statistical small-scale properties. Our work can be seen as a first attempt to develop smart-Lagrangian forcing/drag mechanisms to control turbulence.

physics.flu-dyn↗

arXiv2019

A-priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes

The statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo are investigated during the kinematic, nonlinear and statistically saturated stages. We carry out an a priori analysis of data obtained from an ensemble of direct numerical simulations on $512^3$ grid points and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS) modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, we consider the SGS stress tensors originating from inertial dynamics, Lorentz force and the magnetic induction separately. We find that all SGS energy transfers display some degree of intermittency as quantified by the scale-dependence of their respective probability density functions. Concerning the inertial dynamics, a depletion of intermittency occurs in presence of a saturated dynamo.

physics.flu-dyn↗

arXiv2018

Multiscale properties of Large Eddy Simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier-Stokes equations (NSE), we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the sub-grid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the subleading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.

physics.flu-dyn↗

arXiv2018

Energy transfer in turbulence under rotation

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C) manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where $k_z\ne0$. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices.

physics.flu-dyn↗

arXiv2018

Non-universal behaviour of helical two-dimensional three-component turbulence

The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong helical forcing, the out-of-plane component ceases to behave as a passive advected quantity and develops a nontrivial dynamics which deeply changes its large-scale properties. We show that a small-scale helicity injection correlates the input on the 2D component with the one on the out-of-plane component. As a result, the third component develops a non-trivial energy transfer. The latter is mediated by homochiral triads, confirming the strong 3D nature of the leading dynamical interactions. In conclusion, we show that the out-of-plane component in a 2D3C flow enjoys strong non-universal properties as a function of the degree of mirror symmetry of the small-scale forcing.

physics.flu-dyn↗

arXiv2017

Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations

We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.

physics.flu-dyn↗

arXiv2016

Phase and precession evolution in the Burgers equation

We present a phenomenological study of the phase dynamics of the one-dimensional stochastically forced Burgers equation, and of the same equation under a Fourier mode reduction on a fractal set. We study the connection between coherent structures in real space and the evolution of triads in Fourier space. Concerning the one-dimensional case, we find that triad phases show alignments and synchronisations that favour energy fluxes towards small scales --a direct cascade. In addition, strongly dissipative real-space structures are associated with entangled correlations amongst the phase precession frequencies and the amplitude evolution of Fourier triads. As a result, triad precession frequencies show a non-Gaussian distribution with multiple peaks and fat tails, and there is a significant correlation between triad precession frequencies and amplitude growth. Links with dynamical systems approach are briefly discussed, such as the role of unstable critical points in state space. On the other hand, by reducing the fractal dimension $D$ of the underlying Fourier set, we observe: i) a tendency toward a more Gaussian statistics, ii) a loss of alignment of triad phases leading to a depletion of the energy flux, and iii) the simultaneous reduction of the correlation between the growth of Fourier mode amplitudes and the precession frequencies of triad phases.

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