Evolution of two-dimensional waves in externally perturbed flow on a vertical cylinder

We numerically investigate in a laboratory frame the evolution of waves on the surface of fluid flowing down a cylinder in the context of a two-dimensional Kuramoto-Sivashinsky equation. The conditions for convective instability of the system are derived. We show that spiral waves emerge when the flow is driven at the inlet with a combination of spiral driving and random noise. In the case of a purely-noise-driven flow, spiral-like structures appear occasionally as short transients while the main pattern is a straight wave. In most cases the flow tends to be irregular.