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 inner cylinder increased outer fixed. In two PEO elastic number $$E \in \left\{ 0.16 ; 0.30 \right\} $$ , first instability circular Couette appears as spirals propagating opposite directions along axis cylinders. Just above onset pattern, localized solitons strong radial inflow called flame-like appear abruptly inside waves. The abrupt apparition signature subcritical transition turbulence. flows follows a Gaussian distribution at given Ta number. averaged increases it saturates soliton (flame-pattern) created amplitude exceeds critical value. amplitudes flame patterns law described by mathematical model based on an error function probability observe (flame-pattern). statistical data are used order determine stability curve analysis completed characterization spatiotemporal properties.