Effects of spatially varying slip length on friction drag reduction in wall turbulence

A series of direct numerical simulation has been made of turbulent flow over hydrophobic surfaces, which are characterized by streamwise periodic micro-grooves. By assuming that the size of micro-grooves is much smaller than the typical length-scale of nearwall turbulent structures, the dynamical boundary condition is expressed by a mobility tensor, which relates the slip velocity and the surface shear stress. Based on the derived mathematical relationship between the friction drag and different dynamical contributions, it is shown how the turbulence contribution can be extracted and analyzed.