Analytic Simulations For Wave Propagation Over Submerged Three-dimensional Axisymmetric Quasi-idealized Bathymetries

This thesis studies wave scattering by two types of seabeds which are submergedthree-dimensional axi-symmetrical quasi-idealized bathymetries. The so-called quasi-idealized bathymetry means that the water depth profle equals to a power functionof the radial distance plus a constant, and if the constant is zero, the bathymetry iscalled idealized. Because of this added constant, it becomes more difcult to constructanalytical solutions to linear wave equations such as the long-wave equation (LWE) andthe mild-slope equations (MSE).In the frst part of this thesis, the propagating of long waves over a quasi-idealizedaxi-symmetrical dredge excavation pit is studied. By using variable separation techniqueand series expansion method, an analytical solution to the LWE is constructed, whichis an extension of the analytical solution of Niu and Yu (2011) for an idealized dredgeexcavation pit.In the second part, wave scattering by an axi-symmetrical shoal is studied. Thesame problem were previously studied by scholars for waves restricted in the long-waverange, for example, Zhang and Zhu (1994), Zhu and Harun (2009), Niu and Yu (2011),Liu and Xie (2011). Here, the wave range is extended to the entire wave range and theexplicit modifed mild-slope equation (EMMSE) is employed by Liu and Zhou (2014). Byintroducing a new variable transform, together with the variable separation techniqueand series expansion method, an analytical solution in terms of Taylor series to theEMMSE is obtained.It is worth indicating that, frst, the present solution is an exact solution to theEMMSE since both the equation and the wave dispersion relation are not approximated.Second, the success to transform the implicit MMSE into the EMMSE relies on the useof the independent variable kh which is a common physical parameter. In this thesis,a new transform t=exp(kh) is further introduced which expands the convergencerange of the series solution. Third, the validity of the present solution to the EMMSEis the entire wave range. Because of this advantage, our solution can be comparednot only with Williams et al.’s experimental data of kh=3, but also with Suh etal.’s experimental data of kh=1,2,3. It is clear that all the waves studied in these experiments are beyond the long-wave range.