Research On The Eigen Frequencies And Oscillating Modes Of The Coupled Multi Harbor Basins

Free-surface oscillations and currents can be extremely severe inside a harbor if the wave motions match the natural frequencies of the harbor,leading to detrimental effects on harbor operation and vessel movement.The natural frequencies of a harbor depend on the harbor shape and topography.Reasonable design of the harbor can reduce the possibility of a match between the natural frequencies of the harbor and the frequency range of local incident wave,which would be good to minimize the influence of harbor oscillations.Therefore,the study of harbor oscillations is important for the better design of harbors.The extended mild-slope equation and Boussinesq equation are used to investigate the eigen frequencies and resonant modes of a harbor.The extended mild-slope equation is solved by the finite element method which can simulate the complicated boundary shape well and this model is used to obtain the harbor response under regular waves with various frequencies.The well-known open source code,Funwave2.0 model,is developed based on a fully nonlinear Boussinesq equation.That model is used to study the influence of nonlinearity on the harbor resonance.Both the numerical models above are verified by analytical solution or experimental data.The following problems are studied:(1)The mild-slope equation and Boussinesq equation are used to simulate the extreme modes of harbor resonance in three aspects.The first one is the formation mechanism of extreme modes.The second one is the difference between extreme modes.The last one is the influence of nonlinearity on extreme modes.The numerical results show that the wave energy rise very slowly inside the harbor because of the special flow filed excited by extreme modes,resulting in an extremely long time for the development of extreme modes.The difference between extreme modes depends on the harbor shape.The more closed a harbor is,the more severe the response of extreme modes will be.Nonlinearity can significantly reduce the response of extreme modes and the time to reach steady state.(2)The mild-slope equation is used to simulate the oscillation of a narrow-long harbor with variable depth connected to a semi-circular bay with constant depth.Numerical model test shows that incident waves and the radiation damping of narrow-long harbor are changed due to the bay which affect the resonant features of harbor.Correlation analysis shows that the bay plays a leading role in the coupled resonance if the ratio of water volume between bay and harbor is much higher than 2.5,resulting in a positive correlation between the amplification diagrams of junction and harbor not only in intensity but in trend.Conversely,bay and harbor hold equal status in the coupled oscillation,leading to a positive correlation only in intensity.(3)The oscillations of harbors with connected rectangular basins are investigated by the mild-slope equation,focusing on the change of amplification diagram and modes.The numerical results show that the characteristic length scale of a harbor will be increased because of the newly built rectangular basin,leading to the decrease of frequencies of those resonant modes along the long side of the harbor.The ordinary modes may turn into extreme modes and vice versa.Since the extreme modes are unlikely to become fully developed in reality,it's beneficial that the ordinary modes may turn into extreme modes.In order to obtain a more reasonable assessment of harbor oscillations,the incident wave spectra must be considered.For instance,the harbor response could be very weak in some frequency ranges.By specially designing,those ranges can include the main peak of the incident wave spectra so the harbor response would be weak which can improve the mooring condition inside the harbor.