A non-invasive acoustical method to measure the mean roughness height of the free surface of a turbulent shallow water flow

In this paper, the directivity of the airborne sound field scattered by a dynamically rough free flow surface in a flume is used to determine the mean roughness height for six hydraulic conditions in which the uniform depth of the turbulent flow. The nonlinear curve fitting method is used to minimize the error between the predicted directivity and directivity data. The data fitting algorithm is based on the averaged solution for the scattered sound pressure as a function of angle which is derived through the Kirchhoff integral and its approximations. This solution takes into account the directivity of the acoustic source. For the adopted source and receiver geometry and acoustic frequency it is shown that the contribution from the stationary phase point (single specular point on the rough surface) yields similar results to those which can be obtained through the full Kirchhoff's integral. The accuracy in the inverted mean roughness height is comparable to that achieved with an array of conductive wave probes. This method enables non-invasive estimation of the flow Reynolds number and uniform flow depth.