Study of Turbulent Mixing in a Channel Flow by Numerical Tracking of Material Surfaces

Abstract: A property of turbulent mixing, i.e. stretching of material surfaces, in a wall-bounded flow is examined through the direct numerical simulation (DNS) of a turbulent channel flow. Statistics of a stretching rate and a fractal dimension on the material surface are presented. A series of DNS has been performed with various initial conditions of the surfaces in order to discuss the influence of the wall on mixing. The stretching rate JA, normalized by the Kolmogorov time WK, of a material surface in the core region is comparable to that in homogeneous isotropic turbulence. However the asymptotic value for sufficiently extended surfaces is JA =0.1(WK min)-1 corresponding to one-third of the value (0.3WK-1) for the homogeneous turbulence reported by Goto & Kida [J. Fluid Mech. 586, 59 (2007)]. The fractal dimension of the surface investigated here through the box-counting procedure increases with time until it attains the asymptotic value of 2.39 ± 0.03