Numerical Simulation of the Solitary Waves Propagation and Run-up in Shallow Water

Abstract

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.