Analysis of Scattered Acoustic Signals to Characterise the Behaviour of the Free Surface of Shallow Water Flows

Non-invasive measurement techniques for monitoring free-surface flows in open channels and partially filled pipes are becoming increasingly popular. This paper reports on instrumentation that was used to investigate the Doppler spectra of airborne ultrasonic waves that are back-scattered from the rough free-surface of shallow turbulent water flows. An acoustic measurement technique has been developed and tested in a laboratory flume for a range of flow regimes (Reynolds number based on the mean depth averaged velocity and mean water depth varying between 5,600 and 48,800). The results show that the patterns of the rough water surface travel at the velocity close to the mean surface flow velocity. These patterns are believed to originate from the direct interaction between the free-surface and the turbulence in the flow. Additional surface waves are also observed that propagate at velocities typical to gravity-capillary waves in shallow water. A numerical model based on the Kirchhoff integral and Monte Carlo method has been developed in order to provide a better understanding of the acquired data. The comparison between the experimental results and the predictions from the model suggests that the power spatial spectrum of the free-surface follows a power law function of the wavenumber with exponent -2, which stands for all measured flow regimes. The results have implications for the interpretation of Doppler spectra from acoustic and radio wave back scatter instrumentation which is used to measure the surface flow velocity and hence channel/conduit flow rate.