Transition to turbulence or to periodic patterns in parallel flows. (January 2023)

• Record Type: Journal Article
• Authors: Pomeau, Yves; Le Berre, Martine
• Is Part Of: Chaos, solitons and fractals. Volume 166(2023)
• Publication Date: 2023-01
• Subjects: Turbulence -- Subcritical bifurcation -- Emmons spots -- Amplitude equations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.113019
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We propose a scenario for the formation of localized "turbulent" spots in transition flows, which is known as resulting from the subcritical character of the transition. We show that it is not necessary to add "by hand" a term of random noise in the equations, in order to describe the existence of long wavelength fluctuations as soon as the bifurcated state is beyond the Benjamin–Feir instability threshold. We derive the instability threshold for generalized complex Ginzburg–Landau equation which displays subcriticality. Beyond but close to the Benjamin–Feir threshold we show that the dynamics is mainly driven by the phase of the complex amplitude which obeys Kuramoto–Sivashinsky equation. As already proved for the supercritical case, the fluctuations of the intensity are smaller than those of the phase and slaved to the phase. On the opposite, below the Benjamin–Feir instability threshold, the bifurcated state does lose the randomness associated to turbulence so that the transition becomes of the mean-field type as in noiseless reaction–diffusion systems and leads to pulse-like patterns. Highlights: A directed percolation scenario of transition to turbulence is presented. A deterministic framework for subcritical turbulence is proposed without extra noise. Benjamin–Feir phase instability explains turbulence in subcritical spots.