Analytic Simulations For Interfacial Waves Propagating Submerged Idealized Truncated And Un-idealized Pit In The Two-layer Fluid Shoal

Interfacial waves is a fuctuation of occurring in the stably stratifed fuid. Due tochanges in temperature and salinity, density stratifcation of seawater is an importantfeature of the ocean. However, changes in the sea level pressure feld, uneven seabedtopography, tidal infuence and undersea earthquake are all capable of creating internalwaves in the ocean, so internal waves occur in the stratifed ocean interior is a commonphenomenon. Sometimes the internal waves would have a huge impact on the hydro-dynamic characteristics of the ocean and coastal structures. Hence, it is signifcant tostudy the propagation of interfacial waves. In2005, based on the variational principle,Chamberlain and Porter [26] derived a mild-slope equation for interfacial waves in two-layer fuid, which can degenerates into the long-wave equation for waves in the long-wavelimit. This provides a theoretical base for us to conduct analytical modeling. However,it is not easy to solve the related long-wave equation exactly.In this thesis, the scattering of interfacial waves by a truncated idealized shoal withthe water depth being a power function is frstly investigated. By introducing a variabletransform and using series expansion, an analytical solution to the long-wave equation inthe form of Taylor series is constructed. It is shown that the analytical solution convergesin the whole hump region without any additional restriction to the hump submergence.The comparison among the present solution, Longuet-Higgins’s analytical solution forsurface waves propagation over a submerged cylinder [29] and Liu and Li’s analyticalsolution for surface waves propagation over a submerged truncated shoal [28] shows thecorrectness of our solution. Secondly, an analytical solution to the long-wave equationin the form of Frobenius series for interfacial waves propagating over a submerged un-idealized axi-symmetrical pit is constructed and its correctness is validated against theprevious known numerical solutions. Finally, the infuence of the ratio of densities, theratio of the upper and lower layer water depths, the hump(or pit) dimension and thesubmergence of the shoal and pit on wave amplifcation is investigated and discussed.