Boundary layer of elastic turbulence

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, the elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically statistics of the polymer conformation, which is highly nonuniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of mean flow to the magnitude of flow fluctuations. The ratio is determined by polymer concentration, radius of gyration of the polymers and their length in fully extended state. The results of our asymptotic analysis reproduce the qualitative features of the elastic turbulence at a finite Weissenberg number.