Analytical Simulation And Theoretical Analysis Of Longitudinal Oscillations Within A Rectangular Harbor Over An Idealized Or Un-idealized Slope

Harbor is a partially enclosed water with one or more openings connected to the opensea. If wave motions inside a harbor are forced at one or more of its natural frequencies, theharbor oscillation may occur due to resonance. This oscillation may last a long time becauseof the partial enclosure of the harbor and leads to un-stability and damage of ships.Though harbor resonances were observed in a very early time and studied by many schol-ars, analytical solutions are rare. The main reason comes from a fact that the related governingequation is very complicated for uneven harbor bed. To simplify the governing equation, ina few obtained analytical solutions and approximate analytical solutions, the water depth wasassumed to be either infinite deep or constant. Due to the lack of analytical solutions for vari-able water depth, it is very hard to conduct theoretical analysis to the efect of the variation oftopographies on harbor oscillations.In this thesis, for rectangular harbors over two kinds of slopes with variable water depth,analytical solutions for harbor oscillation in an closed form and in an series form are con-structed, respectively.Firstly, we consider a narrow rectangular harbor with its bed being an arbitrary idealizedslope, i.e., the water depth within the harbor is assumed to be a power function with arbitrarypower exponent, and in the outer open sea, the water depth is assumed to be constant. By usinga skillful variable transform, the long-wave equation in the harbor region can be transformedinto the classical Euler equation or Bessel equation, therefore an analytical solution in closedform for the amplification factor of harbor oscillation is given. Based on this solution, theinfluence of harbor seabed on longitudinal oscillation is analyzed.Secondly, we consider a narrow rectangular harbor with its bed being an arbitrary un-idealized slope, i.e., the water depth within the harbor is assumed to be a constant plus apower function with arbitrary power exponent, and in the outer open sea, the water depthis also assumed to be constant. Diferent from the first case, the governing equation cannotbe transformed into a classical equation, series solution technique must be employed. UsingTaylor series expansion technique together with variable transform, an analytical solution inTaylor series form is constructed. Based on this solution, the influence of both harbor seabed and incident waves on longitudinal oscillation is analyzed.