Nonlinear Stability of a Thin Viscoelastic Film Down a Vertical Wall: A Numerical Study

We numerically investigate the dynamics of a thin viscoelastic liquid flowing down a vertical wall, based on the earlier study of Cheng et al. (J. Phys. D: Appl. Phys., vol. 33, 2000, 1674–1682). They discussed only the linear and weakly nonlinear stability analysis. However, nonlinear effects are more important when the amplitude of the disturbance is small but finite, and therefore, a nonlinear study is very much essential. Further, based on the linear and weakly nonlinear study of Zhao and Jian (Physica Scripta, vol. 96, 2021, 055214), we numerically present the effect of odd viscosity in this case. We also identify how energy transfers from the basic state to the disturbance in this case. Our numerical results support the analytical predictions of the linear and weakly nonlinear theories.