Transformation And Attenuation Of Nonlinear Long Waves Over Permeable Shelf

The nonlinear long waves are common phenomena in water areas. The amplitude of this kind of waves increase sharply when propagating from deep to shallow water which might cause severely damage. In order to investigate the characteristics of the shoaling of nonlinear long waves, the various aspects of the propagation of long waves onto a shelf are examined experimentally and numerically.Firstly, based on a set of Boussinesq equation, the fission process for a solitary waves over an abrupt and a sloping shelf are investigated numerically, highlighting the influences of slope, water depth and incident wave height. The results show that fission process is related to non-linear character. The fission process is more easily to happen at milder slope, on which wave non-linear character is slightly enhanced. The solitary wave with larger incoming wave height or smaller water depth-including deep and shallow water depth-has stronger non-linear character and more easily to disintegrate into several waves which have larger wave height.Secondly, the shoaling of landslide-generated impulse waves are investigated in a wave flume, especially focus on the transformation and attenuation of impulse waves over a permeable shelf. Several tests are conducted under systematic variation of model parameters, the permeability of step, the step thickness, and the non-linear character of waves. Results show that the fission will happen both on an impermeable and a permeable shelf and the wave period will increase which reflect the importance of dispersivity during propagation. The leading soliton reduces its amplitude while propagating on a permeable shelf, but fission process isn’t modified by the permeable shelf and the amplitude of second soliton is not reduced in a short propagation distance. The permeable step with larger thickness has a stronger wave damping and dispersivity become more important. The wave with stronger non-linear character reduces leading soliton amplitude more quickly but permeability still has little influence on the fission process, the amplitude of second soliton and the wave period in a short distance.Finally, using appropriate Boussinesq equations, the transformation of impulse waves propagate on a plane bottom and a permeable shelf are examined numerically in a long distance. The results show that the decrement of impulse waves on a plane bottom is caused by the frequency dispersion and evolution of impulse waves will turn to stable eventually. Impulse waves on a permeable step will decay to zero at a slowing speed rate.