The application of the KdV type equation in engineering simulation

Abstract

Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations and later discrete solitons are strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the initial mean bore height. The complete disintegration of the initial bore into a train of solitons requires very long propagation, but unfortunately, these required distances are usually not available in experimental tests of nature. Therefore, the analysis of the bore decomposition for experimental data into solitons is complicated and requires different approaches. Previous studies have shown that by applying the nonlinear Fourier transform based on the Ko- rteweg–de Vries equation (KdV-NFT) to bores and long-period waves propagating in constant depth, the number and height of all solitons can be reliably predicted already based on the initial bore-shaped free surface. Against this background, this study presents the systematic analysis of the leading-soliton amplitudes for non-breaking and breaking bores with different strengths in different water depths to validate the KdV-NFT results for non-breaking bores to show the limitations of wave breaking on the spectral results. The analytical results are compared with data from experimental tests, numerical simulations and other approaches from the literature.