Lattice Boltzmann Method for Marangoni forcing soap film

Marangoni surface tension forcing soap film is numerically solved by Lattice Boltzmann Method (LBM). A delicate false force term in the LBM equation is proposed to describe the Marangoni forcing soap film. The validity of LBM is elucidated by the linear theory of surface tension profile as a function of the vertical position of the soap film. The effect of thickness on the statistical behaviors of the Marangoni forcing soap film is discussed from three aspects: the energy spectrum, energy transfer and intermittency. It is found that the scaling behavior of energy spectrum is independent of the scaling constant of thickness alpha where the range of alpha is from 0.2 to 0.3. The scaling behavior of energy spectrum is k-5/3, which is in accordance with the Kraichnan theory in the inverse cascade. In the large-scale range, the energy flux cascades to the small scale which is called as a forward cascade process. In this scale range, more energy flux cascades to the small scale when the value of alpha becomes larger. On the contrary, the backward cascade is involved in the small-scale range of the thinned film where more energy transfers to the large scale as the value of alpha is smaller. The intermittency measured by PDF of the velocity increment exists in the turbulent soap film. The universal scaling law of the velocity structure function is identical with the 3D S-L intermittency model and our 2D intermittency theory.