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.
Highlights
IntroductionThe Doppler spectra of the signals of the airborne radar backscattered by the ocean water surface have been studied extensively in the past with the aim of characterizing the amplitude, period, and direction of the ocean waves. Backscattered Doppler spectra are generally dominated by the Bragg scattering mechanism, which produces a stronger backscattering from the surface waves with the wavelength of approximately half the wavelength of the incident scattering wave. In the microwave or airborne ultrasonic range of frequencies, the surface waves that are responsible for Bragg scattering are short capillary ripples, which are subject to modulations by longer waves or by the flow current. This complicates the interpretation of the measurements, especially in rivers where the dynamics of short waves are still largely unknown.In rivers, estimations of the mean flow velocity near the surface can be obtained based on a delay-Doppler analysis applied to ultra high frequency radar in a bistatic configuration. With this technique, the limited time delay resolution impedes the measurement of the longer waves that propagate parallel to the flow direction, which dominate the spectrum of the surface patterns, eliminating the advantages of forward scattering over backscattering. The scattering of ultrasound is easier to study and interpret compared to radio wave scattering due to the absence of polarization
The effects of the different parameters of the dynamic water surface model [namely, the horizontal scale, represented by k0, the vertical scale r, the slope of the surface spectrum a, and the directional distribution D~ ðbÞ] on the acoustic Doppler spectra are discussed, based on the numerical predictions obtained by means of the Kirchhoff model
Across the tested range of flow conditions, the results show the existence of a link between the acoustic Doppler spectra and the characteristic spatial and dynamic scales of the water surface fluctuations
Summary
The Doppler spectra of the signals of the airborne radar backscattered by the ocean water surface have been studied extensively in the past with the aim of characterizing the amplitude, period, and direction of the ocean waves. Backscattered Doppler spectra are generally dominated by the Bragg scattering mechanism, which produces a stronger backscattering from the surface waves with the wavelength of approximately half the wavelength of the incident scattering wave. In the microwave or airborne ultrasonic range of frequencies, the surface waves that are responsible for Bragg scattering are short capillary ripples, which are subject to modulations by longer waves or by the flow current. This complicates the interpretation of the measurements, especially in rivers where the dynamics of short waves are still largely unknown.In rivers, estimations of the mean flow velocity near the surface can be obtained based on a delay-Doppler analysis applied to ultra high frequency radar in a bistatic configuration. With this technique, the limited time delay resolution impedes the measurement of the longer waves that propagate parallel to the flow direction, which dominate the spectrum of the surface patterns, eliminating the advantages of forward scattering over backscattering. The scattering of ultrasound is easier to study and interpret compared to radio wave scattering due to the absence of polarization. In the microwave or airborne ultrasonic range of frequencies, the surface waves that are responsible for Bragg scattering are short capillary ripples, which are subject to modulations by longer waves or by the flow current.6 This complicates the interpretation of the measurements, especially in rivers where the dynamics of short waves are still largely unknown. Estimations of the mean flow velocity near the surface can be obtained based on a delay-Doppler analysis applied to ultra high frequency radar in a bistatic configuration.13,14 With this technique, the limited time delay resolution impedes the measurement of the longer waves that propagate parallel to the flow direction, which dominate the spectrum of the surface patterns, eliminating the advantages of forward scattering over backscattering.. The use of a narrowband signal in the forward scattering configuration eliminates the issue of time delay resolution, and the wide directivity allows the simultaneous observation of the surface behavior over a large area of the rough surface, including the region near the point of specular reflection where the signal-to-noise ratio is maximum
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