Simulations of turbulent channels with prescribed velocity profiles

Direct numerical simulations of turbulent channels with artificially prescribed velocity profiles are discussed, using both natural and purposely incorrect profiles. It is found that turbulence develops correctly when natural profiles are prescribed, but that even slightly incorrect ones modify the Reynolds stresses substantially. That is used to study the dynamics of the energy-containing velocity fluctuations. The stronger (weaker) structures generated by locally stronger (weaker) mean shears have essentially correct isotropy coefficients but they are out of energy equilibrium, with the energy imbalance compensated by turbulent diffusion. The velocity scale in smooth profiles changes with the distance to the wall, and is best described by a friction velocity derived from the local total tangential stress. The behaviour across sharper shear jumps is more consistent with non-equilibrium eddies that relax over wall-normal distances of the order of the distance to the wall, suggesting that the energy equilibrium in the logarithmic layer is not local to a given height, but applies to extended layers homogenized by wall-normal fluxes. Examples of that non-local character are the large-scale inactive fluctuations near the wall, whose velocities do not scale with the local shear stress, but with that of their active 'cores' farther away from the wall.