| When surface waves propagate from deep water to shallow water, they are transformedby reflection, refraction and difraction until they break and dissipate. Physical experiments,numerical simulations and analytical solutions are three commonly used methods to modelwave propagation, in which analytical solutions are widely used in theoretical analysis and tovalidate numerical solutions due to their high accuracy, low cost and time saving.Ocean surface waves can be divided into three bands according to its wavelength, that is,long waves, intermediate waves and short waves. It is clear that the long wave equation is onlyavailable for long waves. In analytical models constructed in this thesis, the modified mild-slopeequation (MMSE) is used as the governing equation and the mass-conserving jump conditionswill be used as the boundary conditions at common boundaries between two adjacent domains.Thus our analytical models can not only be used to model steep terrains with their slopes beingas high as5.67:1, but also cover the whole wave range from long waves (or shallow water) toshort waves (deep water). Two bathymetries will be considered, the first one is submergedtruncated idealized breakwaters and the second one is a submerged truncated idealized shoal.By using the explicit modified mild-slope equation (EMMSE) in the space of spectrum,series solutions to the EMMSE for waves from shallow water to deep water scattered by thesubmerged truncated idealized breakwater and by the submerged truncated idealized shoalare constructed, and the convergence analysis of these two series solutions is conducted. It isshown that the agreement between the present analytical solution based on the MMSE andprevious long-wave analytical solution. Based on the present analytical solution, influence ofvarious factors associated with the submerged breakwater to the reflection efect is analyzed.Also, influence of the dimensions of the submerged shoal to wave amplification is also analyzed. |
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