Numerical modeling of a turbulent boundary layer over a moving wavy surface

Theoretical investigation of a turbulent boundary layer formed over a uniformly moving sinusoidal-shaped wavy plate is presented. The primary objective of this study is twofold: first to report the theoretical treatment of the considered flow and second to investigate and quantify the potential impacts of the surface non-flatness on the turbulent boundary-layer characteristics. Boundary-layer characteristics, such as the boundary-layer thickness, momentum thickness, coefficient of skin friction, and the shape factor, have been formulated into the form of the similarity variables. Theoretical modeling is based on the boundary-layer assumption imposed on the Reynolds-averaged Navier-Stokes equations. Numerical solution is obtained due to the Keller-Box method after implementing the mixing-length turbulence model. Significant contribution of surface waviness in enhancing the momentum transport across the boundary layer is noted, in accordance with the laminar flow. However, such enhancement is much pronounced in the turbulent boundary layer in comparison to the laminar one. Momentum transport is seen to be strengthened by almost 23% in comparison to a flat plate case. Local and average coefficient of skin-friction and the other boundary-layer characteristics are computed for various values of the amplitude-to-wavelength ratio parameter to express its impactful role on the overall flow phenomenon.