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Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number Re = 3000 reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien-Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a solution family that is nonlinearly self-sustained by viscoelasticity. The ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear TS mode, and increases strongly with Weissenberg number, Wi. For the latter, there is a transition in the scaling of this ratio as Wi increases, and the Wi at which the nonlinear solution family comes into existence is just above this transition. Finally, evidence indicates that this branch is connected through an unstable solution branch to two-dimensional elastoinertial turbulence (EIT). These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the Tollmien-Schlichting mode.
Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J.Fluid Mech. 893, A3 (20
Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting (TS) mod
Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks.
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonl
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations. Although similar