Abstract
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.
Highlights
Turbulent, shallow water flows form a common class of flow typical to gravel bed rivers, overland flows and drainage pipes
The airborne acoustic waves generated by the source with directivity pattern of a piston in the rigid baffle are applied to study the statistics of the rough surface of shallow water flow in open channels
It is shown that a straightforward inversion technique based on the single stationary phase point approximation can be used to deduced the mean roughness height of the surface of a turbulent flow
Summary
Shallow water flows form a common class of flow typical to gravel bed rivers, overland flows and drainage pipes. It is shown that for a given source and receiver geometry and Gaussian statistics of the rough surface process, one can estimate the mean sound pressure in the scattered field through the modified expression for the contribution from one specular reflection point taken on the equivalent smooth surface with which the rough surface can be replaced. This transformation enables the use of a relatively straightforward minimisation procedure to retrieve the mean roughness height from the measured angular dependence for the sound pressure above a dynamically rough water-air interface for a range of flow conditions.
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