arXiv subjects

Alvaro Meseguer

Publications and source records attributed to Alvaro Meseguer.

6 recordsLinked to original sources

arXiv2026

Emergence of chaos and fractality in the basin boundary of subcritical shear flow

From a dynamical systems perspective of subcritical transition in shear flows, the basin boundary separating the laminar and turbulent attractors, along with the edge state that governs the long-term dynamics on that boundary, are of fundamental interest. As the Reynolds number is increased from small values, a multiplicity of simple exact coherent structures (ECS) appear in phase space, of which one often undertakes the role of the edge state. At higher values of the Reynolds number, however, the dynamics on the basin boundary and the edge state are sensitive to initial conditions, as shown by a wealth of numerical and experimental studies. The mechanism behind this transition remains unclear. To address this, we examine the subcritical regime of Taylor-Couette flow using a minimal computational box and reveal a generic mechanism whereby the edge state becomes chaotic. The first step in this process involves the formation of a heteroclinic tangle between a travelling-wave-type ECS and an independently engendered chaotic saddle. The interaction causes the basin boundary to incorporate the saddle, thus inheriting its fractal structure, while the edge state itself remains the simple ECS. The transition of the edge state to chaos requires a second step: the formation of a heteroclinic cycle involving the ECS and the chaotic saddle. In consequence, the observation of a simple non-chaotic edge state at given values of the parameters is no guarantee that the same situation will hold at nearby values.

physics.flu-dyn↗

arXiv2026

The stability of electronic Poiseuille flow in two-dimensional materials

Motivated by the experimental observation of electronic Poiseuille flow in graphene [J.A. Sulpizio et al. Nature 576, 75 (2019)] we analyze the linear stability of plane-Poiseuille flow of electrons in a two-dimensional material using a modified Orr-Sommerfeld equation. We calculate the critical current needed to make the flow unstable as a function of the experimental parameters and characterize the most favorable situation, that is the one needing the lowest current density, to observe flow instability. We predict the streamwise wavenumber and frequency at which the instability occurs and discuss the difficulties of an experiment aimed at probing this phenomenon.

cond-mat.mes-hall↗

arXiv2025

Feigenbaum universality in subcritical Taylor-Couette flow

Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor-Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows.

physics.flu-dyn↗

arXiv2025

Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow

The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier-Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs.

nlin.CD↗

arXiv2012

Hopf bifurcation with zero frequency and imperfect SO(2) symmetry

Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyze the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width, and partial breaking of SO(2) to Zm, are also considered. Previous and new experimental and numerical studies of pinned rotating waves are reviewed in light of the new theoretical results.

math.DS↗

arXiv2000

Threshold amplitudes for transition to turbulence in a pipe

Although flow in a circular pipe is stable to infinitesimal perturbations, it can be excited to turbulence by finite perturbations whose minimal amplitude shrinks as R goes to infinity (R = Reynolds number). Laboratory experiments have appeared to disagree with one another and with theoretical predictions about the dependence of this minimal amplitude on $R$, with published results ranging approximately from $R^{-1/4}$ to $R^{-3/2}$. Here it is shown that these discrepancies can be explained by the use of different definitions of amplitude by different authors. An attempt is made to convert the existing results to a uniform definition of amplitude, the nondimensionalized $L^2$ definition common in the theoretical literature. Although subtleties in the physics raise some questions, agreement appears to be reached on a minimal amplitude that scales as $R^{-3/2 \pm 0.3}$.

physics.flu-dyn↗