Introduction of non-uniformity through linearization of the system governing turbulent, mixing of a scalar quantity in a 2-d mixing layer

Abstract

The introduction of mathematical non-uniformity in the formulation of the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow using Goertler's [ZAMM 22 (1942) 244] perturbation argument is discussed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, and then linearized using Goertler's method. Though successful for the mean velocity field, the regular expansion yields inconsistent solutions for the transport of a scalar. Sources of the non-uniformity are identified using appropriate numerical methods for both non-linear and linear formulations. A consistent result is obtained by rescaling the independent variable and equation system and identifying dominant behavior. The results of this corrected formulation are shown to be consistent with the relationships obtained by the author using an approximate matched asymptotic expansion procedure.