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Tollmien-Schlichting Route to Elastoinertial Turbulence

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TURW04 - Wall-bounded turbulence: beyond current boundaries

Recent studies of channel and pipe flows of dilute polymer solutions at Reynolds numbers Re~1000-10000 have revealed a viscoelasticity-driven chaotic flow state denoted elastoinertial turbulence (EIT).  Computations indicate that EIT displays tilted sheetike layers of polymer stretch with weak spanwise-oriented flow structures – a sharp contrast to the 3D quasistreamwise vortex structures that make up inertia-driven Newtonian turbulence. Direct simulations of two-dimensional channel flow of a FENE -P fluid have revealed the existence of a family of flows that is nonlinearly self-sustained by viscoelasticity with structure closely related to the classical Tollmien-Schlichting (TS) wave.  At Reynolds number Re=3000, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch.  At fixed Weissenberg number, Wi, and increasing Reynolds number from 3000-10000, this attractor goes from displaying a sheet of weak polymer stretch to an extended sheet of very large polymer stretch. This evolution arises from the coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cat’s eye structure of the TS wave exceeds 1/2. At Re=10000, the Newtonian TS wave evolves continuously into the EIT state as Wi is increased from zero to about 13. The multilayer structure emerges through a ``sheet-shedding” process by which the individual sheets  break up to form the layered multisheet structure characteristic of EIT .   Finally, having established the connection between the TS wave solution and EIT , we consider the question of how low in Reynolds number this solution family persists. At Wi=30, we find that the viscoelastic TS wave (EIT) solution family persists down to Re between  below 200.  These results may be related to observations of non-laminar flow in polymer solutions at Reynolds numbers below the Newtonian transition threshold.

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