The extended Prandtl closure model applied to the two-dimensional turbulent classical far wake

Abstract

Prandtl’s mixing length closure model has been used extensively in turbulent wake flows. Although the simplicity of this model is advantageous, it contains mathematical and physical limitations. In particular, this model results in a poor estimation of the flow on the center-line and near the wake boundary. Prandtl constructed an improved model, which will be referred to as the extended mixing length model, in an attempt to address many of the limitations of the original model. In this work, the extended Prandtl model is considered. A similarity solution that leaves both the governing equation for the stream-wise mean velocity deficit and the conserved quantity invariant is obtained. The governing partial differential equation is reduced to an ordinary differential equation. The ordinary differential equation,which must be solved subject to appropriate boundary conditions and the conserved quantity, cannot be solved analytically and thus a double-shooting method is developed to obtain the stream-wise mean velocity deficit. A plot of the mean velocity deficit is then produced.