Abstract
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 gravity-capillary 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.
Highlights
The study of the free surface of the sea has received considerable attention in the past
The results reported here support hypothesis (i), that the dispersion relation of the free surface of a shallow turbulent flow with homogeneous static bed roughness can be predicted by including the velocity profile in the derivation of the linearized equations, further investigations would be needed in order to clarify the observed behaviour
The frequency-wavenumber spectra of the free surface fluctuations in a shallow turbulent flow have been compared with a model of small amplitude waves in a rotational flow with the 1/3 power function velocity profile
Summary
The study of the free surface of the sea has received considerable attention in the past. Since the fundamental work of Miles[1] and Phillips,[2] the various mechanisms that allow the wind to produce characteristic patterns of gravity-capillary waves have been well known. The understanding of these phenomena facilitated greatly the development of remote monitoring techniques, which thereafter became a formidable aid to the study of ocean dynamics.[3] In comparison with the surface of the ocean, the free surface of shallow flows such as rivers and in manmade open channels is less understood.
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