Similarity solutions of Prandtl mixing length modelled two dimensional turbulent boundary layer equations

Abstract

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no Blasius type similarity solutions (special exact solutions) have ever been found. In the light of Blasius’ pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and for a special case of flow modelled by Prandtl mixing-length, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. The ordinary differential equation is numerically solved and some useful quantities are produced. For numerical calculations, a complete Maple code is provided.

Keywords

• Turbulent boundary layers
• Laminar boundary layers
• Similarity transformation
• Similarity solution
• Prandtl mixing length
• Reynolds number