We investigate a weakly nonlinear equation that arises in the modelling of wave dynamics on a liquid film flowing down an inclined plane when a turbulent gas flows above it. The model is the Kuramoto-Sivashinsky equation with an additional non-local term multiplied by a parameter representing the relative importance of the turbulent gas. The non-local term has a dispersive effect, destabilising effect on long waves and stabilising or destabilising effect on short waves depending on whether the gas flows downwards or upwards. We investigate the influence of this term on the dynamics of the Kuramoto-Sivashinsky equation by extensive numerical experiments. When the gas parameter is sufficiently large, the solution evolves into a row of weakly interacting pulses.
|Number of pages||12|
|State||Published - 1 Jan 2014|
|Event||IUTAM Symposium on Nonlinear Interfacial Wave Phenomena from the Micro- to the Macro-Scale - Limassol, Cyprus|
Duration: 14 Apr 2013 → 17 Apr 2013