Defect-mediated turbulence in ribbons of viscoelastic Taylor-Couette flow

Abstract

Transition to defect-mediated turbulence in the ribbon patterns observed in a viscoelastic Taylor-Couette flow is investigated when the rotation rate of the inner cylinder is increased while the outer cylinder is fixed. In four polymer solutions with different values of the elasticity number, the defects appear just above the onset of the ribbon pattern and trigger the appearance of disordered oscillations when the rotation rate is increased. The flow structure around the defects is determined and the statistical properties of these defects are analyzed in the framework of the complex Ginzburg-Landau equation.

Vortex merging and splitting: A route to elastoinertial turbulence in Taylor-Couette flow

“…The spectra confirm the behavior observed also in the flow and frequency maps (Fig. 3), namely, that the RSW state is a superposition of waves of various frequencies, several of which have comparable amplitudes, and that this combination of waves transitions to EIT upon increasing Re [11]. One of the RSW spectral peaks corresponds to f = f e , where f e is the elastic wave frequency [7,12,19], as also seen in Fig.…”

“…In the TVF regime [S1, Figure 4 proves that MST does not require shear thinning as in DMT [11] and is not an effect of a transient behavior due to the finite 0 value. They occur in a purely elastic fluid and during steady-state experiments.…”

“…In the presence of inertia (higher Re), elastic fluids are subject to elastoinertial instabilities, leading to the existence of nonaxisymmetric flow states such as ribbons (RIBs) [11] or rotating standing waves (RSWs) [10,12,13]. Gradual transitions from such flows to elastoinertial turbulence (EIT), through a series of increasingly chaotic flow states, have been reported in the literature [13,14].…”

“…Notably, in shear-thinning and elastic polyethylene oxide solutions, an interesting defect behavior of the RIB spirals has been observed [11]. It has been shown that the multiplications of such defects when increasing the rotation speed of the inner cylinder lead to the flow transitioning to EIT through a process called defect mediated turbulence (DMT) [11].…”

Taylor–Couette flow of polymer solutions with shear-thinning and viscoelastic rheology

“…For dilute suspensions with very weak elasticity, De/Re ≤ 0.023, the elasticity has a non-monotonic effect on the critical Reynolds numbers for various flow regimes, but these do not differ significantly from those seen in the Newtonian case (Dutcher & Muller 2011). At slightly higher elasticity, De/Re 0.1, the flow transitions from circular Couette flow to an unsteady state, characterised by standing waves (Groisman & Steinberg 1996;Baumert & Muller 1999;Dutcher & Muller 2013), 'disordered oscillations' (Groisman & Steinberg 1996, elastic turbulence (Liu & Khomami 2013) or 'spiral' or 'ribbon' states (Thomas et al 2006;Latrache et al 2016). At higher values of De/Re, a purely elastic instability occurs, which is independent of Reynolds number (Groisman & Steinberg 1998) and is characterised by isolated vortex pairs called 'diwhirls' (Groisman & Steinberg 1997;Kumar & Graham 2000;Lange & Eckhardt 2001).…”