Scale by scale budget in viscoelastic wall turbulence

Despite the growing interest on the subject, many of the efforts to the comprehension of practical aspects of turbulence in dilute polymer solutions, such as drag reduction, have proven inconclusive, suggesting that, even from the point of view of applications, a more fundamental approach is required. Recently the influence of polymers on the turbulent cascade has been studied in the contest of homogeneous and isotropic turbulence. Those results allowed for the identification of a scale below which the flux towards polymers is larger than the nonlinear transfer. More relevant for the real problems is the study of wall turbulence where the alteration of the energy cascade might have a large effect. On the basis of the DNS data for the turbulent channel flow, an analysis of the interaction between polymers and turbulence at different distances from the wall is provided. A detailed balance of the scale by scale budget of the turbulent kinetic energy is shown.