The effect of surface gravity waves on the measurement of river surface velocity

Optical methods are increasingly used as a means to determine the flow velocity at the surface of rivers. If applied in the absence of visible physical tracers (e.g., floating debris), current methods must rely on the assumption that the water surface deformations are directly advected by the river flow. This assumption is weak in the presence of gravity waves, which propagate in various directions at their own speed. To investigate the properties and effects of these waves, we record videos of a small, shallow river, in the absence of significant wind. Using the image intensity as a proxy for the surface elevation, we demonstrate the presence of gravity waves on the free surface by means of a space-time Fourier analysis. The dominant wavelength in all directions closely matches the wavelength of stationary waves with the front perpendicular to the flow direction. This observation is in accordance with previous laboratory studies. This suggests that the waves originate from the interaction of the flow with the rough bed, and that they are a feature of shallow flows over rough beds. Characteristic ring-wave patterns emerge in the space-time correlation. They are related with a periodic fluctuation of the peak correlation, usually associated with the mean surface velocity. The effect will impact on standard optical surface velocimetry methods if applied to flows without visible floating tracers, but knowledge of gravity waves dynamics can be exploited to infer time averaged characteristics of the river flow.