Bifurcation Model of Laminar-Turbulent Transitions Near Flat Walls

Abstract

In this article, we describe a new mathematical model (bifurcational turbulence model) and justify its suitability for the prediction of laminar and turbulent boundary layer characteristics. The main specific feature of the model is the laminar-turbulent transition, arising as a new solution of the equation for Reynolds stresses, closing the system of Reynolds-averaged Navier-Stokes (RANS) equations. The article is divided into three main parts. The first part describes the RANS and second-order closure conditions together with the premises that we use to obtain the model equations in the closed form. In the second part, we derive the equations of the turbulent-flow model in the shear layer. In the third part, we consider the boundary-layer turbulence transition over a flat plate and present the results of numerical simulations compared with the experimental data.