arXiv subjects

A. Armaroli

Publications and source records attributed to A. Armaroli.

6 recordsLinked to original sources

arXiv2021

Modulational instability in optical fibers with randomly-kicked normal dispersion

We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.

physics.optics↗

arXiv2020

Reconciling different formulations of viscous water waves and their mass conservation

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge choice for the velocity vector is made that cancels the rotational contribution in the kinematic boundary condition, at the cost of rotational velocity in the bulk and a rotational pressure. The third set circumvents the problem by introducing two domains: the irrotational bulk and the vortical boundary layer. This comparison puts forward the link between rotational pressure on the surface and vorticity in the boundary layer, addresses the existence of nonlinear vorticity terms, and shows where approximations have been used in the models. Furthermore, we examine the conservation of mass for the three systems, and how this can be compared to the irrotational case.

physics.flu-dyn↗

arXiv2020

Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping

We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation of the spectrum. In the latter, only the fundamental frequency and the upper and lower sidebands are retained. Plane wave solutions to the NLSE exhibit modulation instability (MI) within a frequency band determined by a linear stability analysis. For modulation frequencies inside the MI-band, we experimentally demonstrate that forcing and damping cause a separatrix crossing during the evolution. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general. When the system is damped by the viscosity of the water, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside the separatrix. Furthermore, for modulation frequencies outside the conventional MI-band, we experimentally demonstrate that contrary to the linear prediction, we do observe a growth and decay cycle of the plane-wave modulation. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution.

nlin.PS↗

arXiv2019

Single-spectrum prediction of kurtosis of water waves in a non-conservative model

We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher order Nonlinear Schrödinger equation (NLS). During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted.

physics.flu-dyn↗

arXiv2016

Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis.

nlin.PS↗

arXiv2011

Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.

nlin.PS↗