Analysis of spectral energy transfer in connection with turbulent drag reduction by polymer

Wavelet multiresolution analysis is used to investigate physical connections between polymer drag reduction and spectral energy transfer in viscoelastic turbulent flows. Direct numerical simulation of viscoelastic channel flow is performed at the friction Reynolds number of 145 at dilute polymer concentrations. Polymers are modeled by the finitely extensible nonlinear elastic model and assumed highly flexible. Newtonian counterpart is also simulated for comparison. Variations of turbulence kinetic energy (TKE) due to interactions between polymer solutions and turbulence are evaluated locally in space and in scale, parameterized by wall-normal locations. Larger structures become more energetic in viscoelastic flow, while smaller eddies are weakened regardless of the distance from the wall. In the viscous sublayer, the net result of these two opposing factors leads to smaller TKE for viscoelastic flow, resulting in drag reduction. Interactions between turbulence and polymers are a strong function of scale and wall-normal location $y^+$; polymers absorb TKE from near-wall regions and store it as elastic energy at $y^+ \lesssim 20$, while they enhance TKE in the log layer.