Theoretical and experimental studies of three-dimensional wavemaking in narrow tanks, including nonlinear phenomena near resonance

Abstract

In view of several practical ramifications of this problem, computational-analytical techniques for calculating waves induced by heaving arbitrary bodies in narrow tanks have been developed, including nonlinear wave groups produced near tank resonance. These feature computational near-field solutions matched with appropriate far-field solutions. In the linear case, the far field is provided by linear mode superposition. In the nonlinear case, the far field is described by a suitable nonlinear evolution equation of the cubic Schrödinger type. Matching techniques were developed. Calculations were successfully carried out and the results confirm the important effect of tank walls on added mass and damping.Results of computations have been compared with some data obtained with a conical wavemaker in a narrow tank. Pronounced nonlinear wave groups were obtained near resonance, and these are well reproduced in some detail by the nonlinear theory and computations, without considering any effects of dissipation.The related problem of resonant wave groups produced by a segmented paddle wavemaker has also been treated by analysis and subject to computation, with good general agreement with past experiments. The technique features matching near- and far-field computations using energy considerations.