The spectrum of the acoustic waves backscattered by the dynamic rough surface of a shallow water flow

Scattering of airborne ultrasonic waves by the moving rough surface of a shallow water flow is a poorly explored topic. In particular, acoustic wave scattering from the free-surface of shallow water flows such as rivers or open-channels has been relatively neglected. Most of the existing studies focus on backscattering from the ocean surface, where Doppler spectra have been used to recover useful information on the wind-generated waves1. These works are based largely on electromagnetic waves. For flows in hydraulically narrow, prismatic channels it is expected that the surface roughness is generated mainly by the action of turbulence inside the water flow, and the roughness pattern is largely two-dimensional and dominated by the dispersive nature of waves. The existing studies on shallow flows are limited to the measurement of the Doppler spectra of backscattered electromagnetic waves with the aim of determining the velocity of the flow. In this paper we will show how the analysis of Doppler spectra of airborne ultrasonic backscattered waves could be used in order to obtain useful information on the characteristics of the turbulencedriven surface roughness and its dynamics, which could eventually improve our understanding of the interaction between turbulence and the free-surface in a turbulent, open channel flow