Image analysis of thickness in flowing soap films. I: effects of polymer

Two-dimensional turbulence in flowing soap films with polymer additives is analyzed by image analysis. The power spectra of the interference patterns of turbulent soap films are calculated. The scaling exponent of the power spectrum is −5/3 for polymer free solution and −1 for dilute polymer solution in enstrophy cascade range, which is consistent with the results of thickness fluctuations in previous researches. We propose a Curvature analysis method that calculates the curvatures of the interference pattern of turbulent soap films. The results suggest that the curvature histogram describes well the shape of the interference pattern, which is related to the shape of the vortices. The curvature histograms for different polymer concentrations can be fitted by a stretched exponential function.