Experimental and theoretical study of stationary nonlinear three-dimensional wave regimes on a straight rivulet flowing down an inclined plane

Wavy flow of straight rivulets down an inclined plate was studied experimentally and theoretically. Instantaneous three-dimensional shape of a rivulet was obtained experimentally using Brightness-Based Laser-Induced Fluorescence technique. The results were compared to the predictions by quasi-two-dimensional theoretical model. The model reproduces well the transition of wave pattern from soliton-like to sinusoid-like waves with increasing wave frequency, as well as the main wave characteristics such as shape, amplitude and velocity. The agreement gets worse for overall Reynolds number of 252, where the local thickness-based Reynolds number is large enough for turbulence to start. The discrepancy also grows with the rivulet width, since the region where turbulence develops is getting larger. In such conditions, the experimentally observed waves may acquire additional small-wave perturbations of their rear slopes and deep troughs across the slopes. Such perturbations are substantially three-dimensional and their prediction requires more complex theoretical models.