Application Research On Mathematical Model Of Marine Disaster Based On N-S Equations In Different Simplified Forms

China is a marine big country whose coastline is abundance and sea area is vast. All kinds of marine disasters not only create massive losses of our country economy, but also threaten the life safety of coastal residents and seafaring personnel. There are many different kinds of marine disasters, tsunami, storm surge, marine oil spill are the three typical dynamical and environmental marine disasters. The research on mathematical model of marine disaster can provide a basis for the scientific warning of different kinds of marine disasters.The basis of marine disaster mathematical model is to establish a high precision hydrodynamic field and attach new field action according to the reasons of different disasters. This paper systematically derives the vertical integration form of 3D Navier Stokes equations and proposes a concept that marine disaster mathematical model is a combined model which combined with different governing equations, considerations and discrete methods. From this point, four types of the marine disaster mathematical models have been established in this paper.(1)The discrete forms and governing equations of several kinds of marine disaster mathematical models have been systematically summarized. ADI discrete form, discrete process of finite element and modeling process of SPH have been introduced through the storm surge disaster, marine oil spill disaster and two-dimensional vertical numerical model of oil-water motion. Through tsunami mathematical model, the wave model which governing equation is Boussinesq equation has been introduced. Through storm surge and marine oil spill model the hydrodynamic model which governing equation is shallow water circulation equations has been introduced.(2) Local tsunami mathematical model of Japan tsunami in 2011 has been built. The local tsunami mathematical model consists of the initial displacement field model of tsunami source and tsunami wave propagation model. The initial fields of different kinds of submarine topographies have been considered.According to the Equal Water Mass Method which means the water and submarine topography change in volume is equal, the round and long-narrow deformation volume factor have been determined. The governing equation of tsunami wave propagation is Boussinesq equation. The discrete form is ADI and the term of energy changes as the form of radiation stress has been supplemented which can simulate the tsunami wave propagation energy transfer progress. The simulated results and observed results fit well.(3) Huanghai and Bohai Sea storm surge mathematical model has been built.This model applies shallow water circulation equation as the governing equation of tidal current calculation. The wind field and the wave field calculated by the SWAN model have been considered. The water increased affected by the wave radiation stress on storm surges has been studied. The results show that the effects of radiation stress on the flow rate is obvious and has little effect on the water level.(4) Two-dimensional vertical numerical model of oil-water motion basing on SPH method has been built. The oil slick motion of above water, underwater and under wave condition has been studied. The effects of different densities, different viscosities on the results of oil-water motion pattern have been discussed. The density redistribution method and transition particle method has been proposed which can improve the oil-water two-phase flow model. The extended scale and time calculated by this model have been compared with the Fay model results and the correlation coefficient is 0.998.(5) Luanjiakou Harbor marine oil spill mathematical model has been built.Tidal current, wind wave, oil slick and other motion factors have been taken into account in the model. The motion patterns of oil slick boundary and boundary adsorption on sea areas with many islands have been proposed. The thickness of oil volatilization and spread out has been considered in the oil slick edges. The oil slick adsorption has been considered on shorelines and islands. Thirty oil spill scenarios have been simulated by this model including different dynamic conditions, spills positions, oil types and the modes of oil spill. The trajectories and coverage area of different scenarios have been analyzed.