Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary Data on the frequency-wavenumber spectra and dispersion relation of the dynamic water surface in an open channel flow are very scarce. In this work, new data on the frequency-wavenumber spectra were obtained in a rectangular laboratory flume with a rough bottom boundary, over a range of subcritical Froude numbers. These data were used to study the dispersion relation of the surface waves in such shallow turbulent water flows. The results show a complex pattern of surface waves, with a range of scales and velocities. When the mean surface velocity is faster than the minimum phase velocity of gravity-capillary waves, the wave pattern is dominated by stationary waves that interact with the static rough bed. There is a coherent three-dimensional pattern of radially propagating waves with the wavelength approximately equal to the wavelength of the stationary waves. Alongside these waves, there are freely propagating gravity-capillary waves that propagate mainly parallel to the mean flow, both upstream and downstream. In the flow conditions where the mean surface velocity is slower than the minimum phase velocity of gravitycapillary waves, patterns of non-dispersive waves are observed. It is suggested that these waves are forced by turbulence. The results demonstrate that the free surface carries information about the underlying turbulent flow. The knowledge obtained in this study paves the way for the development of novel airborne methods of non-invasive flow monitoring. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Over the last two decades, interest in the free-surface behaviour of gravity-driven shallow turbulent flows has increased considerably. It is believed that observation of free-surface behaviour can provide useful information about the hydrodynamic characteristics of the flow and enable remote retrieval of these characteristics to non-invasively and rapidly monitor river flows. At the current state the literature presents scattered knowledge and also exhibits non-uniformity in the terminology used. This paper is a review of the state-of-art of this area of research and was created with two objectives: to gather the information relevant to understand the linkages between the free-surface behaviour and underpinning hydrodynamic processes while using a uniform terminology, and to analyse the gaps in our knowledge of this critical topic.

Noncontact measurement techniques are increasingly used to monitor rivers, especially in flood events, when traditional flow gauging techniques are difficult to apply (e.g., Le Coz et al., 2010;Perks et al., 2016). Existing noncontact techniques have been used almost exclusively for measuring the surface flow velocity pattern, using radar or ultrasound scattering from the water surface (e.g.,

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.