Meandering instability of a rivulet on a partially wetting incline

It is common to observe small rivulets in sinks or on window-panes which follow sinuous paths (stationary or not) instead of flowing down along the direction of steepest slope. A laboratory experiment shows that these meandering rivulets exist only for certain ranges of the control parameters (flow rate and substrate inclination). The geometrical properties of the resulting paths can be understood in terms of force balances between inertia, capillarity and contact line pinning. The nature of the instability, i.e. why the straight rivulet becomes unstable, however remains unclear. We study the rivulet near the onset for meandering to understand the role of noise and surface defects.