In 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.

This work is focused on numerical simulation of the interaction of a solitary surface wave with a submerged rectangular breakwater in the constant depth model basin using the non-hydrostatic hydrodynamic model SWASH (Simulating WAves till SHore). The features of the transformation of a wave passing over an obstacle with the width and height changes of the breakwater were investigated. Based on numerical experiments, the transformation coefficients for the soliton and the zone of its attenuation area behind a breakwater were calculated. The localization of the region of maximum attenuation of the wave passing beyond the breakwater is determined. The analysis of the spatial structure features of free-surface fluctuations caused by the interaction of a soliton with a breakwater is carried out. The depthaveraged orbital fluid velocities are calculated and the dependence of their values and directions on the geometric parameters of the underwater obstacle is determined.

The paper is aimed at investigating the propagation of solitons in a shallow basin, assessing the nonlinear effects resulting from the wave run-up on a gentle coast, and at comparing the estimates obtained using different numerical models with the available analytical dependencies. Methods and Results. The results of numerical simulations carried out using two nonlinear models of long waves (the author's model and the Simulating WAves till SHore (SWASH) one) are represented in the paper. The solitary wave profiles were obtained during its propagation in the part of a basin with constant depth conjugated with the inclined bottom. The process of a wave run-up on the coast was simulated using the algorithm of fluid movement along a dry coast. It is shown that when a soliton propagates in the basin part with constant depth, the nonlinearity effects are manifested in deformation of a wave profile. In other words, increase of the wave initial amplitude and the distance traveled by a wave is accompanied by growth of the wave front slope steepness. This, in its turn, leads to increase of a splash when the waves run-up on the coast. The estimates of the run-up heights resulted from different numerical models are in good agreement. Conclusions. The calculated values of the maximum wave run-up on the coast for the non-deformed waves, the length of which is equal to that of the traversed path, are close to the estimates obtained analytically. For the waves with the deformed profile, the front slope steepness of which increases with propagation over long distances, the run-up heights increase with growth of the wave initial amplitude. In such a case, it is desirable to replace the analytical estimates with the numerical ones. The run-up height of the deformed waves can exceed the wave initial amplitude by four or more times. The results obtained in this study can be useful in projecting the coastal protection constructions with the regard for preserving the coastal ecology and economy.