Doppler spectra of airborne ultrasound forward scattered by the rough surface of open channel turbulent water flows

Abstract

Experimental data are presented on the Doppler spectra of airborne ultrasound forward scattered by the rough dynamic surface of an open channel turbulent flow. The data are numerically interpreted based on a Kirchhoff approximation for a stationary random water surface roughness. The results show a clear link between the Doppler spectra and the characteristic spatial and temporal scales of the water surface. The decay of the Doppler spectra is proportional to the velocity of the flow near the surface. At higher Doppler frequencies the measurements show a less steep decrease of the Doppler spectra with the frequency compared to the numerical simulations. A semi-empirical equation for the spectrum of the surface elevation in open channel turbulent flows over a rough bed is provided. The results of this study suggest that the dynamic surface of open channel turbulent flows can be characterized remotely based on the Doppler spectra of forward scattered airborne ultrasound. The method does not require any equipment to be submerged in the flow and works remotely with a very high signal to noise ratio.

Reconstruction of the Frequency-Wavenumber Spectrum of Water Waves With an Airborne Acoustic Doppler Array for Noncontact River Monitoring

“…Figures 2d, e, and f were obtained for a surface with a broadband powerfunction spectrum Ψ(κ) ∼ κ −3 , 10π ≤ κ ≤ 100π, and with the root-mean-squared (rms) surface elevation of 0.3 mm. A similar power-function dependence of the surface spectrum on κ has been previously proposed and validated for open-channel flow applications based on measurements of acoustic scattering [11], [14]. The surface parameters used for the simulations in the present work ensured the validity of the small-roughnessamplitude approximation.…”

“…Turbulent forcing can modify the speed of water waves [12] or generate additional wave patterns [13] making the identification of the Doppler velocity and their link with the underlying depth-averaged flow velocity nontrivial [4], [11]. Measurements with a bistatic geometry (separate source and receiver) allow focusing on longer and more predictable waves while increasing the signal-to-noise ratio, but at the expense of the ease of data interpretation [8], [14]. The main obstacle to the interpretation of the Doppler spectra for river monitoring is the fact that waves with different wavelengths, speeds, and/or directions of propagation can produce a peak at the same Doppler frequency [11].…”

Using Noncontact Measurement of Water Surface Dynamics to Estimate River Discharge

“…This was done a posteriori, with the aid of a numerical model that created synthetic images of the water surface, with a spectrum similar to the ones observed in Figure 11. The synthetic videos were built by a Fourier synthesis method (e.g., Dolcetti & Krynkin, 2017) applied to a simplified spectrum that followed ∼ k −1/4 , with cut‐offs at the wavenumbers k 0 and 2 π /0.05 rad/m. The wavenumber spectrum was transformed into a frequency‐wavenumber spectrum by means of the dispersion relations (Equations and ), using the estimated values of the flow parameters d and U 0 (hence, a posteriori).…”