Skin friction and surface optical flow in viscous flows

The relationship between skin friction and the surface optical flow (SOF) in viscous flows is discussed based on the evolution equations of surface temperature, scalar, and enstrophy, where the SOF is defined as the convection velocity of these quantities. It is found that the SOF is proportional to skin friction, which can be determined by solving the optical flow equation re-cast from these evolution equations. This optical flow method can be applied to surface temperature and mass transfer visualizations to extract skin friction fields in experiments. To examine this method, it is first applied to complex surface enstrophy structures obtained in direct numerical simulation data of a turbulent channel flow. Furthermore, it is applied to surface temperature structures obtained in time-resolved temperature sensitive paint measurements in a flow over a National Advisory Committee for Aeronautics (NACA) 0015 airfoil model and an impinging jet.