Spontaneous generation of spiral waves by a hydrodynamic instability

The coiling of a thin filament of viscous fluid falling onto a surface is a common and easily reproducible hydrodynamic instability. Here we report for the first time that this instability can generate regular spiral patterns, in which air bubbles are trapped in the coil and then advected horizontally by the fluid spreading on the surface. We present a simple model that explains how these beautiful patterns are formed, and how the number of spiral branches and their curvature depends on the coiling frequency, the frequency of rotation of the coiling center, the total flow rate, and the thickness of the spreading fluid film.