We investigate experimentally the freezing of a rivulet, obtained by flowing water on a cold solid substrate (0.C to -35.C). Surprinsingly, we show that a peculiar 3D structure is formed, composed of an ice pyramidal base-layer on which a vertical wall develops.

This structure grows until reaching a stationary shape after tens of seconds. This stationary state is shown to result from the competition between the water cooling and its convection as the growing ice layer lowers the cooling ability of the substrate.