A PROPOSAL OF A VORTICITY ESTIMATION METHOD WITH MLS AND PTV AND ITS APPLIACATION TO FLOWS UNDER WIND WAVES

Abstract

  A method to measure two-dimensional vorticity fields was developed by combining MLS, the Moving Least Square method, with PTV. A velocity vector at a grid point is approximated with a pair of quadratic functions fitted to velocity vectors at particle positions estimated by PTV which randomly distributed around the grid point. The vorticity is calculated by differentiating the quadratic functions. A two-dimensional Gaussian weight function is employed for fitting. The size of the interrogation area is represented with the standard deviation of the weight function. The expression of the optimum size was analytically derived with a coeffient finally determined by Monte Carlo simulation with synthesized velocity fields with random measurement errors. The accuracy of the proposed method was compared with that of a conventional grid based method, which verified superiority of the proposed one. The method was applied to measurement of vorticity distribution generated by wind waves. Three synchronized high-speed video cameras were set beside a wind-wave tunnel: two were used to capture particle images in a wider field of view and one to detect the water surface. Temporal and spatial behaviors of vorticies generated at and near a water surface can be clearly traced by the proposed method.