Nonlinear characteristics of the interaction of a turbulent boundary layer with a wavy surface

A nonlinear interaction of a turbulent boundary layer with a wavy surface of a solid body or a liquid whose level has a deviation in the form of a traveling monochromatic wave is studied. For the waviness of small curvature, a calculation procedure is proposed for the amplitude dependence of the drag coefficient and complex elasticity which characterizes the back action of the flow on the surface inflection. The analysis is based on the use of an isotropic algebraic model of turbulent viscosity and an orthogonal system of curvilinear coordinates that follow the surface inflections. The interaction between the flow and the surface wave is described within the framework of a quasi-linear model, and a two-scale, mean-flow model is used to determine the transverse structure of the flow in a smoothly expanding boundary layer.