arXiv subjects

Miguel Onorato

Publications and source records attributed to Miguel Onorato.

At least 19 recordsLinked to original sources

arXiv2026

Recursive behavior in a diatomic FPUT lattice

We study the diatomic FPUT lattice with cubic anharmonic potential, and analyze the recurrent behaviour of its solutions. We find that two distinct types of recurrence occur. One type is the classic FPUT recurrence; for such recurrence, we find that the relation between recurrence period and nonlinear strength is similar to that in the monatomic case. The other type, which cannot exist in the monatomic lattice, is the recurrence due to the interactions between modes in the two branches of the dispersion relation. Indeed, we prove the existence of the optical-acoustical-acoustical resonant interaction between three Fourier modes for which a recurrent behavior in the distribution of the energy is observed. In addition, we develop a reduced Fourier-space dynamical model that reproduces the same recurrent behavior. We assess the robustness of our results through numerical simulations of the diatomic Toda lattice and the diatomic granular chain; in both cases, the same recursive behavior is observed. Finally, in the continuous limit, we derive from the diatomic model a system of three coupled PDEs which are known to be integrable.

nlin.CD↗

arXiv2026

Cascades in the Kinetic Equation for the Majda-McLaughlin-Tabak model

The Majda-McLaughlin-Tabak (MMT) family of models has proven to be an efficient ground for benchmarking wave turbulence theory, thanks to the low computational cost required to test theoretical ideas and the possibility of tuning nonlinearity and dispersive properties of the equations. Here, we study numerically the wave kinetic equation (WKE) associated with the MMT model and perform simulations to study turbulent cascades. We confirm numerically the predictions of wave turbulence theory, both in the parameter space region where the wave kinetic equation was proven to be well posed and outside of it. We also observe a new stable stationary state in a region where no cascade solutions are expected, a region that, to the best of our knowledge, has not been explored before. Moreover, following recent work, we study next-to-leading-order corrections to the wave kinetic equation; we uncover incurable divergences in the one-dimensional MMT model and, more generally, in higher-dimensional systems with concave power-law dispersion relations.

physics.flu-dyn↗

arXiv2026

Resonant interactions in the $α$-FPUT lattice with site-dependent coefficients

The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains. In this work, we extend this approach to the $α$-FPUT problem when the spring stiffness $χ$ and the nonlinear coefficient $α$ are site-dependent. Although three-wave interactions are non-resonant for constant coefficients, their spatial modulation gives rise to a non-trivial resonant manifold. In this framework, we derive a new kinetic equation that suggests the possibility of substantially faster thermalization with respect to the constant coefficient case. The new kinetic equation includes also an extra term that can be associated to the Bragg-scattering mechanism, which promotes the isotropization of the wave-action spectral density function.

cond-mat.stat-mech↗

arXiv2026

Pseudovorticity of 2+1D optical solitons

In the hydrodynamic representation of a quantum fluid or optical field, vorticity vanishes wherever the phase is well defined, and is instead localized at phase singularities, or quantum vortices. Pseudovorticity, by contrast, characterizes local rotational structures, even in regions without singularities or net orbital angular momentum. We study both experimentally and numerically pseudovorticity in photorefractive solitons and show that a detailed phase and amplitude analysis unveils a complex rotational flow dynamic: bright 2+1D solitons are found to carry a pseudovorticity dipole, while quadrupoles emerge in soliton fusion. The phenomenon, also explained using geometrical considerations, suggests a general picture according to which stable high-dimensional solitons naturally carry a hierarchy of pseudovorticity multipoles, encoded in the local perturbed phase and amplitude.

physics.optics↗

arXiv2026

Revealing wave-wave resonant interactions in ocean wind waves

Ocean wind waves are a fundamental manifestation of complex dynamics in geophysical fluid systems, characterized by a rich interplay between dispersion and nonlinearity. While linear wave theory provides a first-order description of wave motion, real-world oceanic environments are governed by nonlinear interactions that are responsible for a transfer of energy between waves of different lengths. Established theoretical concepts predict that four-wave resonant interactions serve as the primary mechanism for energy transfers among wave components in oceanic surface wave fields. Although the presence and efficiency of these resonant interactions have been demonstrated in controlled wave tank experiments, their direct identification in the real ocean, where a large number of random waves interact, has remained elusive. Here, using a stereoscopic system that enables the measurement of surface elevation in both space and time, we provide experimental evidence of resonant interactions in ocean wind waves. Our data not only reproduce the well-known figure-eight pattern predicted by Phillips, but also reveal a continuum of different resonant configurations that closely match the theoretical predictions. These findings support the validity of third-generation ocean wave models, strengthening their ability to accurately capture wave dynamics in the ocean.

physics.ao-ph↗

arXiv2025

Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves

In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements, however, reveal prominent features that go beyond the predictions of time resonance theory. In this work, we develop a theoretical framework to interpret these signatures by identifying and characterizing an alternative mechanism: space resonances. These arise when wave packets share the same group velocity and remain co-located, leading to long-lived interactions. We further show that gauge-breaking terms in the Hamiltonian give rise to space resonances supported on negative frequencies. By combining sea-surface elevation data, numerical simulations, and analytical theory, we derive the leading-order spatio-temporal spectrum for weakly interacting water waves, providing a unified explanation for its observed features.

nlin.PS↗

arXiv2025

Validity condition of normal form transformation for the $β$-FPUT system

In this work, we provide a validity condition for the normal form transformation to remove the non-resonant cubic terms in the $β$-FPUT system. We show that for a wave field with random phases, the normal form transformation is valid by dominant probability if $β\ll 1/N^{1+ε}$, with $N$ the number of masses and $ε$ an arbitrarily small constant. To obtain this condition, a bound is needed for a summation in the transformation equation, which we prove rigorously in the paper. The condition also suggests that the importance of the non-resonant terms in the evolution equation is governed by the parameter $βN$. We design numerical experiments to demonstrate that this is indeed the case for spectra at both thermal-equilibrium and out-of-equilibrium conditions. The methodology developed in this paper is applicable to other Hamiltonian systems where a normal form transformation needs to be applied.

math-ph↗

arXiv2025

Vortex to Rotons Transition in Dipolar Bose-Einstein Condensates

Recent experimental advancements enabled the creation of various systems exhibiting superfluid behavior, with one notable achievement being the development of dipolar Bose-Einstein condensates (dBECs). When confined along one or more spatial dimensions, these condensates exhibit a dispersion relation reminiscent of superfluid liquid helium, featuring a roton-like minimum. This study investigates the existence of two-dimensional solitary waves in dBECs characterised by topological defects (quantised vortices) and their transition to vortex-free Jones-Roberts solitons. The explicit connection between solitary waves and roton excitation is demonstrated, supporting Feynman's hypothesis regarding the nature of rotons as fading vortex excitations.

cond-mat.quant-gas↗

arXiv2025

On the Wave Kinetic Equation in the presence of forcing and dissipation

The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface gravity waves. Only at the end of the derivation are the non-conservative effects, such as forcing and dissipation, included as additional terms to the collision integral. In this paper, we present a first attempt to derive the wave kinetic equation when the dissipation/forcing is included in the deterministic dynamics. If, in the dynamical equations, the dissipation/forcing is one order of magnitude smaller than the nonlinear effect, then the classical wave action balance equation is obtained and the kinetic time scale corresponds to the dissipation/forcing time scale. However, if we assume that the nonlinearity and the dissipation/forcing act on the same dynamical time scale, we find that the dissipation/forcing dominates the dynamics and the resulting collision integral appears in a modified form, at a higher order.

nlin.CD↗

arXiv2025

Anomalous correlators, negative frequencies and non-phase-invariant Hamiltonians in random waves

We investigate a generic non-phase invariant Hamiltonian model that governs the dynamics of nonlinear dispersive waves. We give evidence that initial data characterized by random phases naturally evolve into phase correlations between positive and negative wavenumbers, leading to the emergence of non-zero anomalous correlators and negative frequencies. Using analytical techniques, we show that anomalous correlators develop on a timescale of $O(1/ε)$, earlier than the kinetic timescale. Our theoretical predictions are validated through direct numerical simulations of the deterministic system.

nlin.CD↗

arXiv2024

Wave Turbulence and thermalization in one-dimensional chains

One-dimensional chains are used as a fundamental model of condensed matter, and have constituted the starting point for key developments in nonlinear physics and complex systems. The pioneering work in this field was proposed by Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. An intense and fruitful mathematical and physical research followed during these last 70 years. Recently, a fresh look at the mechanisms of thermalization in such systems has been provided through the lens of the Wave Turbulence approach. In this review, we give a critical summary of the results obtained in this framework. We also present a series of open problems and challenges that future work needs to address.

nlin.CD↗

arXiv2024

Observations of rogue seas in the Southern Ocean

We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard South African icebreaker S.A.~Agulhas~II. Records include water surface elevation across a range of wave conditions, spanning from early stages of wave growth to full development. We give experimental evidence of rogue seas, i.e., sea states characterizided by heavy tails of the probability density function well beyond the expectation based on bound mode theory. These conditions emerge during wave growth, where strong wind forcing and high nonlinearity drive wave dynamics. Quasi-resonance wave-wave interactions, which are known to sustain the generation of large amplitude rogue waves, capture this behaviour. Wave statistics return to normality as the wind forcing ceases and waves switch to a full developed condition.

physics.ao-ph↗

arXiv2023

Three- and four-wave resonances in the nonlinear quadratic Kelvin lattice

In this paper we investigate analytically and numerically the nonlinear Kelvin lattice, namely a chain of masses and nonlinear springs, as in the alpha-Fermi-Pasta-Ulam-Tsingou (FPUT) chain, where, in addition, each mass is connected to a nonlinear resonator, i.e., a second mass free to oscillate. Both nonlinearities are quadratic in the equations of motion. This setup represents the simplest prototype of nonlinear wave propagation on a nonlinear metamaterial. In the linear case, we diagonalize the system, and the two branches of the dispersion relation can be found. Using this result, we derive in the nonlinear case the equations of motion for the normal variables in Fourier space, obtaining a system governed by triad interactions among the two branches of the dispersion relation. We find that the transfer of energy between these two branches is ruled by three- and four-wave resonant interactions. We perform numerical simulations of the primitive equations of motion and highlight the role of resonances as an efficient mechanism for transferring energy. Moreover, as predicted by the theory, we provide direct evidence that four-wave resonances appear on a time scale that is longer than the time scale for three-wave resonances. We also assess the recurrence behaviour (usual in the FPUT system) for the nonlinear Kelvin lattice, and we show that, while recurrence is observed if all the energy is placed, at time t=0, in the lowest mode of the acoustical branch, a non-recurrent behaviour is observed if the initial energy is located in the optical branch.

nlin.PS↗

arXiv2023

Attenuating surface gravity waves by an array of submerged resonators: an experimental study

We report on an experimental study of a device composed by an array of submerged, reversed and periodic cylindrical pendula (resonators), whose objective is the attenuation of surface gravity waves. The idea is inspired by the concept of metamaterials, i.e. engineered structures designed to interact with waves and manipulate their propagation properties. The study is performed in a wave flume where single frequency waves are excited in a wide range of frequencies. We explore various configurations of the device, measuring the transmitted, reflected and dissipated energy of the waves. If the incoming wave frequencies are sufficiently close to the natural frequency of the pendula, we find a considerable wave attenuation effect, driven by viscous dissipative mechanisms. This behaviour is enhanced by the number of resonators in the array. Moreover, the device is also capable of reflecting the energy of selected frequencies of the incoming waves. These frequencies can be predicted by assuming the interactions involving at least three wave modes, including higher harmonics, and are therefore associated with the distance between the resonators. The presented results show promise for the development of a environmentally sustainable device for mitigating waves in coastal zones.

physics.flu-dyn↗

arXiv2022

Stokes drift and impurity transport in a quantum fluid

Stokes drift is a classical fluid effect in which travelling waves transfer momentum to tracers of the fluid, resulting in a non-zero drift velocity in the direction of the incoming wave. This effect is the driving mechanism allowing particles, i.e. impurities, to be transported by the flow; in a classical (viscous) fluid this happens usually due to the presence of viscous drag forces. Because of the eventual absence of viscosity in quantum fluids, impurities are driven by inertial effects and pressure gradients only. We present theoretical predictions of a Stokes drift analogous in quantum fluids for classical impurities obtained using multi-time analytical asymptotic expansions. We find that, at the leading order, the drift direction and amplitude depend on the initial impurity position with respect to the wave phase; at the second order, dominant after averaging over initial conditions, our theoretical model recovers the classical Stokes drift but with a coefficient that depends on the relative particle-fluid density ratio. Numerical simulations of a two-dimensional Gross-Piteaveskii equation coupled with a classical impurity corroborate our findings. Our predictions are experimentally testable, for instance, using fluids of light obtained in photorefractive crystals.

physics.flu-dyn↗

arXiv2022

Three-dimensional imaging of waves and floe sizes in the marginal ice zone during an explosive cyclone

The marginal ice zone is the dynamic interface between the open ocean and consolidated inner pack ice. Surface gravity waves regulate marginal ice zone extent and properties, and, hence, fluxes between the atmosphere and ocean, and ice advance and retreat. Over the past decade, seminal experimental campaigns have generated much needed measurements of wave evolution in the marginal ice zone, which, notwithstanding the prominent knowledge gaps that remain, are underpinning major advances in understanding the region's role in the climate system. Here, we report three-dimensional imaging of waves from a moving vessel and simultaneous imaging of floe sizes, with the potential to enhance the marginal ice zone database substantially. The images give the direction--frequency wave spectrum, which we combine with concurrent measurements of wind speeds and reanalysis products to reveal the complex multi-component wind-plus-swell nature of a cyclone-driven wave field, and quantify evolution of large-amplitude waves in sea ice.

physics.ao-ph↗

arXiv2022

Anomalous conduction and second sound in the Fermi-Pasta-Ulam-Tsingou chain: wave-turbulence approach

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids like nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e. propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons is described by the wave kinetic equation (WKE), derived directly from the microscopic dynamics. Here, we use the spatially nonhomogeneous WKE of the prototypical $β-$ Fermi-Pasta-Ulam-Tsingou (FPUT) model, equipped with thermostats able to set different temperatures at the two ends. Our main findings are as follows: (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wavenumbers. (ii) The high-wavenumber phonons relax to local thermodynamic equilibrium transporting energy diffusively, {\it à la Fourier}. (iii) The low-wavenumber phonons are nearly noninteracting and transfer energy ballistically; this latter phenomenon is the analogous of the second sound emission, observed for example in superfluids.

cond-mat.mes-hall↗

arXiv2021

Attenuating surface gravity waves with mechanical metamaterials

Metamaterials and photonic/phononic crystals have been successfully developed in recent years to achieve advanced wave manipulation and control, both in electromagnetism and mechanics. However, the underlying concepts are yet to be fully applied to the field of fluid dynamics and water waves. Here, we present an example of the interaction of surface gravity waves with a mechanical metamaterial, i.e. periodic underwater oscillating resonators. In particular, we study a device composed by an array of periodic submerged harmonic oscillators whose objective is to absorb wave energy and dissipate it inside the fluid in the form of heat. The study is performed using a state of the art direct numerical simulation of the Navier-Stokes equation in its two-dimensional form with free boundary and moving bodies. We use a Volume of Fluid interface technique for tracking the surface and an Immersed Boundary method for the fluid-structure interaction. We first study the interaction of a monochromatic wave with a single oscillator and then add up to four resonators coupled only fluid-mechanically. We study the efficiency of the device in terms of the total energy dissipation and find that by adding resonators, the dissipation increases in a non trivial way. As expected, a large energy attenuation is achieved when the wave and resonators are characterised by similar frequencies. As the number of resonators is increased, the range of attenuated frequencies also increases. The concept and results presented herein are of relevance for applications in coastal protection.

physics.flu-dyn↗