Turbulence modelling based on non-Newtonian constitutive laws

International audienceThis work revisits the analogy between Newtonian turbulence and non-Newtonian laminar flows. Several direct numerical simulations (DNS) data of a plane channel flow, for a large range of Reynolds numbers (180 <= Reτ <= 2000) were explored. The profiles of mean velocity and second moment quantities were used to extract viscometric functions in the non-Newtonian modeling framework. The Reynolds stress tensor is expressed in terms of a set of basis kinematic tensors based on a projection of a nonlinear framework. The coefficients of the model are given as functions of the intensity of the mean strain tensor. The apparent eddy turbulent viscosity, the first and second normal stress differences are presented as function of the shear rate. One of the advantages of the new algebraic nonlinear power law constitutive equation derived in the paper, is that is only dependent on the mean velocity gradient and can be integrated up to the wal