Thinking About Several Problems Of Tidal Equations In Rectangular Gulf

Tide is a periodical fluctuation. The tides in a semi-enclosed rectangular estuary canshow the physical properties of the tides in Ocean effectively. By the study of thetides in a semi-enclosed rectangular estuary, the tidal mathematical expressions can beobtained. Combining with the physical background, the conclusion can be made asfollow: the tide is the sum of the Kelvin mode and Poincare mode. This is a great helpfor people who do the related study on similar problems.Firstly, this paper introduced the development and advances of the research on thetides in a rectangular estuary. In1921, Taylor made a study on the tides in arectangular estuary without considering the bottom friction. Fang[1]et al studied theTaylor problem considering linear bottom friction and got the analytical solution ofthe tidal equations.Secondly, this paper made a calculation by using the successive approximationmethod in Fang[1]et al to check Fang^[1]et al’s numerical solutions of the tidalequations. The tidal simulation plottings are obtained. It shows that the amphidromicpoint in the northern hemisphere is towards to the left coast by the friction effect. Thispartly verified the analytical solutions of the tidal equations in Fang[1]et al. However,after examining the tidal current on the roof of estuary, it is found that the numericalsolutions doesn’t satisfy the boundary conditions of the equations, that is, the tidalcurrent is not zero on the roof of estuary, and when the number of the items increases,the tidal current increases.Thirdly, in order to get the numerical solutions of the tidal equations satisfying theboundary conditions, the author use collocation method and Galerkin method whichare part of Method of Weighted Residuals solving the boundary value problems, andget the relevant tidal simulation plottings. It is found that the tidal current approachesto zero as the number of items is big enough and the boundary conditions tend to besatisfied. Furtherly, the comparison of the results between the successive approximation method in Fang[1]et al and collocation method is made. And also thecomparison of the results between the successive approximation method and Galerkinmethod is made. It shows that the numerical results of the successive approximationmethod do not satisfy the boundary conditions near the roof of estuary.