Elastic turbulence in two-dimensional Taylor-Couette flows

Abstract

We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model, also performed at high Weissenberg numbers with the program OpenFOAM. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law Φ ∝ (Wi − Wic) γ with Wic = 10 and γ = 0.45. The power spectrum of the velocity fluctuations shows a power-law decay with a characteristic exponent, which strongly depends on the radial position. It is greater than two, which we relate to the dimension of the geometry.

Active open-loop control of elastic turbulence

“…Furthermore, the Oldroyd-B model has only a single relaxation time, whereas real polymer solutions possess a broad spectrum of relaxation times. Nevertheless, the characteristics of elastic turbulence are observed in numerical simulations of this model 16,55 , indicating that the above simplifications do not qualitatively change the physical behavior. Therefore, numerical simulations provide physical insight in the complex behavior of viscoelastic fluids.…”

“…Although our setting does not access the three dimensions of experimental flows, we can gain general insight into controlling viscoelastic fluids and their response to time-dependent shear. We have shown an elastic instability towards elastic turbulence at in earlier work, where we applied a shear rate constant in time in the same geometry 55 . In this work, we use two kinds of time-modulated shear rates in the form of a square or sine wave, which display similar results.…”

“…Different numerical techniques were employed to solve equations modeling viscoelastic fluids and thereby also revealed the purely elastic instability in similar geometries. Articles address unbounded flows with sinusoidal forcing 6 , 46 , 47 , Kolmogorov flow 48 , 49 , as well as wall-bounded flows, including sudden-expansion flow 50 , channels with cross-slot geometry 51 or serpentines 52 and the Taylor–Couette geometry 53 – 55 . Thus, demonstrating the importance of numerical techniques in understanding the underlying physical principles in complex fluid flows.…”

“…Articles address unbounded flows with sinusoidal forcing 6,46,47 , Kolmogorov flow 48,49 , as well as wall-bounded flows, including sudden-expansion flow 50 , channels with cross-slot geometry 51 open Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany. * email: r.vanbuel@tu-berlin.de or serpentines 52 and the Taylor-Couette geometry [53][54][55] . Thus, demonstrating the importance of numerical techniques in understanding the underlying physical principles in complex fluid flows.…”

Dissipative systems with nonlocal delayed feedback control

“…It also provides an example for double delay systems, which have recently attracted attention [42][43][44]. In future studies we will apply delayed feedback to specific nonlinear soft matter systems such as photoresponsive fluid interfaces [45] and viscoelastic flow in Taylor-Couette geometry [46]. The work presented in this article will help us to categorize the observed spatiotemporal dynamics.…”