arXiv subjects

Francesco Fedele

Publications and source records attributed to Francesco Fedele.

At least 19 recordsLinked to original sources

arXiv2025

Fold catastrophe in breaking waves

We present a dynamical-systems perspective on wave breaking for ideal incompressible free-surface flows. By tracking the most energetic hotspot on the wave surface, we find that near breaking the surface slope m evolves on a fast timescale governed by the small parameter epsilon = (partial_z u)^(-1), the inverse vertical velocity gradient at the hotspot, while the focusing parameter A = (U - Ce)/(U - Creq) varies slowly and adiabatically. Here U is the horizontal fluid velocity at the energetic point, Ce its propagation speed, and Creq the equivalent crest speed. This slow-fast structure reveals a fold catastrophe in the (m, A) space whose boundary forms the geometric skeleton organizing the dynamics near breaking. Finite-time blowup occurs when the trajectory crosses this boundary, marking the onset of breaking. The inception of breaking is further characterized by crossing the slope threshold theta* = arctan(sqrt(2) - 1) = 22.5 degrees. This critical angle marks the maximum anisotropy that can be sustained between the Hessians of the velocity and pressure fields, reflecting an imbalance between kinetic and potential energy fluxes. The anisotropy of the velocity Hessian also gives rise to the classical 30-degree slope observed at the inflection point of steep waves near breaking inception. The crest height is limited by the maximum excess of kinetic over potential energy that the flow can sustain, beyond which breaking becomes inevitable. Wave breaking can also be interpreted as a gravity analogue of a collapsing black hole, with apparent and event horizons representing the onset and inception of breaking.

physics.flu-dyn↗

arXiv2024

Hamiltonian Lorenz-like models

The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz models describing the dynamics of a single variable in a zonally-periodic domain, without dissipation and forcing, conserve energy but are not Hamiltonian. In this paper, we start from a general continuous parent fluid model, from which we derive a family of Hamiltonian Lorenz-like models through a symplectic discretization of the associated Poisson bracket that preserves the Jacobi identity. A symplectic-split integrator is also formulated. These Hamiltonian models conserve energy and maintain the nearest-neighbor couplings inherent in the original Lorenz model. As a corollary, we find that the Lorenz-96 model can be seen as a result of a poor discretization of a Poisson bracket. Hamiltonian Lorenz-like models offer promising alternatives to the original Lorenz models, especially for the qualitative representation of non-Gaussian weather extremes and wave interactions, which are key factors in understanding many phenomena of the climate system.

physics.ao-ph↗

arXiv2023

Geometric Phases of Nonlinear Elastic $N$-Rotors via Cartan's Moving Frames

We study the geometric phases of nonlinear elastic $N$-rotors with continuous rotational symmetry. In the Hamiltonian framework, the geometric structure of the phase space is a principal fiber bundle, i.e., a base, or shape manifold~$\mathcal{B}$, and fibers $\mathcal{F}$ along the symmetry direction attached to it. The symplectic structure of the Hamiltonian dynamics determines the connection and curvature forms of the shape manifold. Using Cartan's structural equations with zero torsion we find an intrinsic (pseudo) Riemannian metric for the shape manifold. One has the freedom to define the rotation sign of the total angular momentum of the elastic rotors as either positive or negative, e.g., counterclockwise or clockwise, respectively, or viceversa. This endows the base manifold~$\mathcal{B}$ with two distinct metrics both compatible with the geometric phase. In particular, the metric is pseudo-Riemannian if $\mathsf{A}<0$, and the shape manifold is a $2$D~Robertson-Walker spacetime with positive curvature. For $\mathsf{A}>0$, the shape manifold is the hyperbolic plane $\mathbb{H}^2$ with negative curvature. We then generalize our results to free elastic $N$-rotors. We show that the associated shape manifold~$\mathcal{B}$ is reducible to the product manifold of $(N-1)$ hyperbolic planes $\mathbb{H}^2$~($\mathsf{A}>0$), or $2$D~Robertson-Walker spacetimes~($\mathsf{A}<0$) depending on the convection used to define the rotation sign of the total angular momentum. We then consider elastic $N$-rotors subject to time-dependent self-equilibrated moments. The $N$-dimensional shape manifold of the extended autonomous system has a structure similar to that of the $(N-1)$-dimensional shape manifold of free elastic rotors. The Riemannian structure of the shape manifold provides an intrinsic measure of the closeness of one shape to another in terms of curvature, or induced geometric phase.

physics.class-ph↗

arXiv2023

Discovery of a novel 1,3,4-oxadiazol-2-one-based NLRP3 inhibitor as a pharmacological agent to mitigate cardiac and metabolic complications in an experimental model of diet-induced metaflammation

Inspired by the recent advancements in understanding the binding mode of sulfonylurea-based NLRP3 inhibitors to the NLRP3 sensor protein, we developed new NLRP3 inhibitors by replacing the central sulfonylurea moiety with different heterocycles. Computational studies evidenced that some of the designed compounds were able to maintain important interaction within the NACHT domain of the target protein similarly to the most active sulfonylurea-based NLRP3 inhibitors. Among the studied compounds, the 1,3,4-oxadiazol-2-one derivative 5 (INF200) showed the most promising results being able to prevent NLRP3-dependent pyroptosis triggered by LPS/ATP and LPS/MSU by 66.3 +/- 6.6% and 61.6 +/- 11.5% and to reduce IL-1\b{eta} release (35.5 +/- 8.8 % μM) at 10 μM in human macrophages. The selected compound INF200 (20 mg/kg/day) was then tested in an in vivo rat model of high-fat diet (HFD)-induced metaflammation to evaluate its beneficial cardiometabolic effects. INF200 significantly counteracted HFD-dependent "anthropometric" changes, improved glucose and lipid profiles, and attenuated systemic inflammation and biomarkers of cardiac dysfunction (particularly BNP). Hemodynamic evaluation on Langendorff model indicate that INF200 limited myocardial damage-dependent ischemia/reperfusion injury (IRI) by improving post-ischemic systolic recovery and attenuating cardiac contracture, infarct size, and LDH release, thus reversing the exacerbation of obesity-associated damage. Mechanistically, in post-ischemic hearts, IFN200 reduced IRI-dependent NLRP3 activation, inflammation, and oxidative stress. These results highlight the potential of the novel NLRP3 inhibitor, INF200, and its ability to reverse the unfavorable cardio-metabolic dysfunction associated with obesity.

physics.bio-ph↗

arXiv2023

On the Effective Mass of Mechanical Lattices with Microstructure

We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective mass. We first revisit a classical case of microstructure being modeled by a spring-interconnected mass-in-mass cell. The frequency-dependent effective mass of the cell is the sum of a static mass and of an added mass, in analogy to that of a swimmer in a fluid. The effective mass is derived using three different methods: momentum equivalence, action equivalence, and dynamic condensation. These methods are generalized to mechanical systems with arbitrary microstructure. As an application, we calculate the effective mass of a $1$D composite lattice with microstructure modeled by a chiral spring-interconnected mass-in-mass cell. A reduced (condensed) model of the full lattice is then obtained by lumping the microstructure into a single effective mass. A dynamic Bloch analysis is then performed using both the full and reduced lattice models, which give the same spectral results. In particular, the frequency bands follow from the full lattice model by solving a linear eigenvalue problem, or from the reduced lattice model by solving a smaller nonlinear eigenvalue problem. The range of frequencies of negative effective mass falls within the bandgaps of the lattice. Localized modes due to defects in the microstructure have frequencies within the bandgaps, inside the negative-mass range. Defects of the outer, or macro stiffness yield localized modes within each bandgap, but outside the negative-mass range. The proposed formalism can be applied to study the odd properties of coupled micro-macro systems, e.g., active matter.

physics.class-ph↗

arXiv2022

On the stability of the laminar boundary layer beneath a Stokes wave

The linear stability of the laminar boundary layer flow of a Stokes wave in deep waters is investigated by means of a 'momentary' criterion of instability for unsteady flows (Blondeaux and Seminara, 1979). In the parameter range investigated, it is found that the flow is stable to 2-D perturbations. The least stable eigenmode of the resulting Orr-Sommerfield spectrum attains its maximum beneath the boundary layer of the Stokes wave. Moreover, an analysis of the associated pseudospectrum indicates that the laminar flow when modified by imperfections is unstable due to the non-normality of the Orr-Sommerfeld operator, and the unstable pseudo-eigenmodes tend to peak within the boundary layer. The laminar flow of the Stokes wave is also stable to 3-D streamwise-independent perturbations. Instability is observed for the laminar flow with imperfections. The associated unstable pseudo-eigenmodes are streamwise vortical rolls similar to Langmuir cells. The laminar boundary layer flow of a Stokes wave appears to be stable to infinitesimal perturbations, but it may likely be unstable to finite perturbations, as in Poiseuille pipe flows. The present results are supportive of the recent experimental evidence of spontaneous occurrence of turbulence beneath unforced non-breaking surface waves.

physics.flu-dyn↗

arXiv2020

Crest speeds of unsteady surface water waves

Intuitively, crest speeds of water waves are assumed to match their phase velocities. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the generic behavior of crest speeds of linear to highly nonlinear unsteady waves. While our major focus is on gravity waves where a generic crest slowdown occurs cyclically, results for capillary-dominated waves are also discussed, for which crests cyclically speed up. This curious phenomenon arises when the theoretical constraint of steadiness is relaxed, allowing waves to change their form, or shape. In particular, a kinematic analysis of both simulated and observed open ocean gravity waves reveals a forward-to-backward leaning cycle for each individual crest within a wave group. This is clearly manifest during the focusing of dominant wave groups essentially due to the dispersive nature of waves. It occurs routinely for focusing linear (vanishingly small steepness) wave groups, and it is enhanced as the wave spectrum broadens. It is found to be relatively insensitive to the degree of phase coherence and focusing of wave groups. The nonlinear nature of waves limits the crest slowdown. This reduces when gravity waves become less dispersive, either as they steepen or as they propagate over finite water depths. This is demonstrated by numerical simulations of the unsteady evolution of 2D and 3D dispersive gravity wave packets in both deep and intermediate water depths, and by open ocean space-time measurements.

physics.ao-ph↗

arXiv2017

Some special solutions to the Hyperbolic NLS equation

The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly acccurate Fourier solver.

physics.class-ph↗

arXiv2017

The sinking of the El Faro: predicting real world rogue waves during Hurricane Joaquin

We present a study on the prediction of rogue waves during the 1-hour sea state of Hurricane Joaquin when the Merchant Vessel El Faro sank east of the Bahamas on October 1, 2015. High-resolution hindcast of hurricane-generated sea states and wave simulations are combined with novel probabilistic models to quantify the likelihood of rogue wave conditions. The data suggests that the El Faro vessel was drifting at an average speed of approximately~$2.5$~m/s prior to its sinking. As a result, we estimated that the probability that El Faro encounters a rogue wave whose crest height exceeds 14 meters while drifting over a time interval of 10~(50) minutes is $\sim1/400$~$(1/130)$. The largest simulated rogue wave has similar generating mechanism and characteristics of the Andrea, Draupner and Killard rogue waves as the constructive interference of elementary waves enhanced by bound nonlinearities.

physics.geo-ph↗

arXiv2016

Kinematics of fluid particles on the sea surface. Hamiltonian theory

We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and traveling waves we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.

physics.ao-ph↗

arXiv2016

Are rogue waves really unexpected?

An unexpected wave is defined by Gemmrich & Garrett (2008) as a wave that is much taller than a set of neighboring waves. Their definition of "unexpected" refers to a wave that is not anticipated by a casual observer. Clearly, unexpected waves defined in this way are predictable in a statistical sense. They can occur relatively often with a small or moderate crest height, but large unexpected waves that are rogue are rare. Here, this concept is elaborated and statistically described based on a third-order nonlinear model. In particular, the conditional return period of an unexpected wave whose crest exceeds a given threshold is developed. This definition leads to greater return periods or on average less frequent occurrences of unexpected waves than those implied by the conventional return periods not conditioned on a reference threshold. Ultimately, it appears that a rogue wave that is also unexpected would have a lower occurrence frequency than that of a usual rogue wave. As specific applications, the Andrea and WACSIS rogue wave events are examined in detail. Both waves appeared without warning and their crests were nearly $2$-times larger than the surrounding $O(10)$ wave crests, and thus unexpected. The two crest heights are nearly the same as the threshold~$h_{0.3\cdot10^{6}}\sim1.6H_{s}$ exceeded on average once every~$0.3\cdot 10^{6}$ waves, where $H_s$ is the significant wave height. In contrast, the Andrea and WACSIS events, as both rogue and unexpected, would occur slightly less often and on average once every~$3\cdot10^{6}$ and~$0.6\cdot10^6$ waves respectively.

physics.ao-ph↗

arXiv2015

On Oceanic Rogue Waves

We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler characteristics of random fields. Extreme statistics of the Andrea rogue wave event are examined capitalizing on European Reanalysis (ERA)-interim data. A refinement of Janssen's (2003) theory suggests that in realistic oceanic seas characterized by short-crested multidirectional waves, homogeneous and Gaussian initial conditions become irrelevant as the wave field adjusts to a non-Gaussian state dominated by bound nonlinearities over time scales $t\gg t_{c}\approx0.13T_{0}/νσ_θ$, where $T_{0}$, $ν$ and $σ_θ$ denote mean wave period, spectral bandwidth and angular spreading of dominant waves. For the Andrea storm, ERA-interim predictions yield $t_{c}/T_{0}\sim O(1)$ indicating that quasi-resonant interactions are negligible. Further, the mean maximum sea surface height expected over the Ekofisk platform's area is higher than that expected at a fixed point. However, both of these statistics underestimate the actual crest height $h_{obs}\sim1.63H_s$ observed at a point near the Ekofisk site, where $H_s$ is the significant wave height. To explain the nature of such extreme, we account for both skewness and kurtosis effects and consider the threshold $h_{q}$ exceeded with probability $q$ by the maximum surface height of a sea state over an area in time. We find that $h_{obs}$ nearly coincides with the threshold $h_{1/1000}\sim1.62H_s$ estimated at a point for a typical $3$-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas.

physics.ao-ph↗

arXiv2015

On the kurtosis of deep-water gravity waves

In this paper, we revisit Janssen's (2003) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves at deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin-Feir index and the parameter $R=σ_θ^{2}/2ν^{2}$, a measure of short-crestedness for the dominant waves with $ν$ and $σ_θ$} denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian type spectrum. For multidirectional or short-crested seas initially homogenous and Gaussian, in a focusing (defocusing) regime dynamic kurtosis grows initially, attaining a positive maximum (negative minimum) at the intrinsic time scale \[ τ_{c}=ν^{2}ω_{0}t_{c}=1/\sqrt{3R},\qquad\mathrm{or}\qquad t_{c}/T_{0}\approx0.13/νσ_θ, \] where $ω_{0}=2π/T_{0}$ denotes the dominant angular frequency. Eventually the dynamic excess kurtosis tends monotonically to zero as the wave field reaches a quasi-equilibrium state characterized with nonlinearities mainly due to bound harmonics. Quasi-resonant interactions are dominant only in unidirectional or long-crested seas where the longer-time dynamic kurtosis can be larger than that induced by bound harmonics, especially as the Benjamin-Feir index increases. Finally, we discuss the implication of these results on the prediction of rogue waves.

physics.flu-dyn↗

arXiv2014

Interval-based parameter identification for structural static problems

We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The inversion consists of a two-step algorithm: first, an estimate of the parameters is obtained by means of a deterministic iterative solver. Then, the algorithm switches to the interval extension of the previous solver, using the deterministic estimate of the parameters as an initial guess. The iterations are terminated based on a new containment-stopping criterion, which is intrinsic to intervals. Various numerical examples show that the proposed method provides guaranteed interval enclosures of the parameters.

math.NA↗

arXiv2014

Geometric phases of water waves

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric and dynamical phase velocities $U_d$ and $U_g$ associated with the parallel transport through the principal fiber bundle of the wave motion with $\mathit{U}(1)$ symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed $c=U_d+U_g$ with $c/U_d\approx0.8$ and $U_{g}/U_d\approx-0.2$.

physics.ao-ph↗

arXiv2014

Hopf fibrations for turbulent pipe flows

We propose a generalization of Hopf fibrations to quotient the streamwise translation symmetry of turbulent pipe flows viewed as dynamical systems. In particular, we exploit the geometric structure of the associate high dimensional state space, which is that of a principal fiber bundle. The relation between the comoving frame velocity $U_{d}$ associated with the dynamical phase of an orbit in the bundle and the Taylor's hypothesis is investigated. As an application, Laser-Induced-Fluorescence techniques are exploited to capture planar fluorescent dye concentration fields tracing a turbulent pipe flow at the bulk Reynolds number $\mathfrak{\mathsf{Re}}=3200$. The symmetry reduction analysis of the experimental data reveals that the speed $u$ of dye concentration bursts is associated with the dynamical and geometric phases of the corresponding orbits in the fiber bundle. In particular, in the symmetry-reduced frame we unveil a pattern-changing dynamics of the passive scalar structures, which explains the observed speed $u\approx U_{d}+U_{g}$ of intense bursting events in terms of the geometric phase velocity $U_{g}\approx0.43U_{d}$ associated with the orbits in the bundle.

physics.flu-dyn↗

arXiv2013

Linking reduced breaking crest speeds to unsteady nonlinear water wave group behavior

Observations show that maximally-steep breaking water wave crest speeds are much slower than expected. We report a wave-crest slowdown mechanism generic to unsteady propagating deep water wave groups. Our fully nonlinear computations show that just prior to reaching its maximum height, each wave crest slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This finding is validated in our extensive laboratory and field observations. This behavior appears to be generic to unsteady dispersive wave groups in other natural systems.

physics.ao-ph↗

arXiv2013

On certain properties of the compact Zakharov equation

Long-time evolution of a weakly perturbed wavetrain near the modulational instability threshold is investigated within the framework of the compact Zakharov equation for unidirectional deep-water waves, recently derived by Zakharov & Dyachenko (2011). Multiple-scale solutions reveal that a perturbation to a slightly unstable uniform wavetrain of steepness μslowly evolves according to a Nonlinear Schrodinger equation. In particular, for small carrier wave steepness μ<μ_1~0.27 the perturbation dynamics is of focusing type and the long-time behavior is characterized by Fermi-Pasta-Ulam recurrence, the signature of breather interactions. However, the amplitude of breathers and their likelihood of occurrence tend to diminish as μincreases while the Benjamin-Feir index decreases and becomes nil at \mu1. Thus, homoclinic orbits persist only for small values of wave steepness μ<<μ_1, in agreement with recent experimental and numerical observations of breathers. When the Zakharov equation is already beyond its range of nominal validity for μ>μ_1, predictions seem to foreshadow a dynamical trend to wave breaking. In particular, the perturbation dynamics becomes of defocussing type, and nonlinearities tend to stabilize a linearly unstable wavetrain as Fermi-Pasta-Ulam recurrence is suppressed. At μ=μ_c~0.577, subharmonic perturbations restabilize and superharmonic instability appears, possibly indicating that wave dynamic behavior changes at large steepness, in qualitative agreement with the numerical simulations of Longuet-Higgins and Cokelet (1978) for steep waves. Indeed, for μ>μ_c a multiple-scale perturbation analysis reveals that a weak narrowband perturbation to a uniform wavetrain evolves in accord with a modified Korteweg-de Vries/Camassa-Holm type equation, again implying a possible mechanism conducive to initiating wave breaking.

physics.flu-dyn↗