Transition to turbulence via flame patterns in viscoelastic Taylor-Couette flow.

Transition to inertio-elastic turbulence in Taylor-Couette flow with shear-thinning and viscoelastic polymer solutions is investigated when the rotation rate of the inner cylinder is increased and the outer cylinder is fixed. In two polymer solutions of PEO with elastic number [Formula: see text], the first instability of the circular Couette flow appears as spirals propagating in opposite directions along the axis of cylinders. Just above the onset of the spirals pattern, the localized solitons of the strong radial inflow called flame-like flow appear abruptly inside waves. The abrupt apparition of the flame-like flow is the signature of the subcritical transition to turbulence. The number of the flame-like flows follows a Gaussian distribution at given Ta number. The averaged number of the flame-like flow increases as the rotation rate is increased and it saturates in the inertio-elastic turbulence. The soliton of the strong radial inflow (flame-pattern) is created when it amplitude exceeds a critical value. The distribution of the critical amplitudes of the flame patterns follows a Gaussian law at given Ta number. The transition to turbulence is described by a mathematical model based on an error function of the probability to observe a strong inflow (flame-pattern). The statistical data of the critical amplitude and the probability to observe the flame patterns are used with the mathematical model in order to determine the stability curve of the transition to turbulence. The analysis of the transition to turbulence is completed by the characterization of the spatiotemporal properties.