Elastic turbulence in a curvilinear channel flow

Abstract

We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal an emergence of the boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width that follows from our early investigations of the boundary layer in elastic turbulence of different flow geometries. The appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow suggests that rare and strong parcels of excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing. And finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts to the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.