Propagation of a Single Long Wave in the Bays with U-Shaped Cross-Section Form

Abstract

AbstractIn the framework of the nonlinear long wave theory, the evolution of a single wave propagating in the bays with U-shaped cross-section is studied. A good conformity was found between the numerical and analytical estimates of the wave height variation along the bay axis. It is shown that the influence of the shape of the bay cross-section on the wave field is manifested in the sea level rise with the approach to the bay periphery. Estimates of vertical run-up and drainage depth of the shore at the bay top with different cross-sectional shape were obtained. It is found that in bays with a triangular cross-sectional shape there are the greatest run-up height and the greatest drainage depths from the shore. The distance traveled by the wave from the bay entrance to the point of wave breaking is the largest for the bay with cross-sectional shape is approximate to rectangular.KeywordsNonlinear long wavesNarrow bays with U-shaped cross-sectionNumerical solutionWave amplificationRun-up of long waves on the shore