arXiv subjects

Roger Ayats

Publications and source records attributed to Roger Ayats.

4 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↗

arXiv2025

From directed percolation to patterned turbulence

The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order reappears when alternating laminar and turbulent regions arrange in regular stripe patterns. This macroscopic organization is believed to arise top down from a classic pattern forming instability of turbulence, imprinting a wavelength onto the disordered flow field. We here demonstrate that patterns instead self-assemble with increasing velocity. Starting from the intermittent stripe regime, specifically from the corresponding directed percolation (DP) critical point, regular patterns are established within the scaling range of the DP transition. Likewise the patterns' expansion rates are set by the DP critical exponents, attesting that all underlying processes are stochastic. This apparent contradiction between the inherent stochasticity and the displayed order is resolved by abandoning the common perception of laminar and turbulence as opposing states. More generally our study exemplifies that macroscopic patterns can arise solely from local stochastic rules, in the absence of wavelength selection typically associated with pattern formation.

physics.flu-dyn↗

arXiv2024

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↗

arXiv2024

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 Poincar\'e 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↗