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Onset of Lagrangian chaos: From fractal power spectrum to the absolutely continuous one
Phys. Rev. Fluids 9, 014401 – Published 18 January, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.014401
Abstract
We study transition to chaotic advection in the fluid motion across a plane rectangular domain with periodic boundary conditions. The flow, induced by a combination of time-independent force with constant pumping in both spatial directions, is equivalent to dynamics on the surface of a 2-torus. At considered force amplitudes, the stationary flow pattern includes the global drift and the localized vortices encircled by separatrices of stagnation points. If the Eulerian velocity field is time-independent and rotation number on the torus, controlled by pumping intensities, is irrational, then the power spectrum of the Lagrangian observables is singular continuous (fractal) and the autocorrelation function of velocity displays no ultimate decay. As the increase of the force destabilizes the stationary flow and replaces it by periodically oscillating velocity field, singularities in the numerically evaluated spectrum disappear, whereas temporal correlations vanish after a certain time interval.
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