Wave propagation over a rectangular trench

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Abstract
An analysis is presented for the propagation of water waves past a rectangular submarine trench. Two-dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The result shows that, for a particular flow configuration, thereexists an infinite number of discrete wave frequencies at which waves are completely transmitted. The validity of the solution in the infinite constant-water-depth region is shown by comparing with the results using the boundary integral method for given velocity distributions along the mouth of the trench. The accuracy of the matching procedure is also demonstrated through the results of the boundary integral technique. In addition, laboratory experiments were performed and are compared with the theory for two of the cases considered.

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