A Finite Volume Model For Global Two-dimensional Ocean Tides On Spherical Block-structured Quadrilateral Grids

Flood and ebb is the rhythm of ocean tides, tidal dynamics is an important component of Geophysical fluid dynamics. It swashes the ocean topography and exerts profound effects on the human activity along the coast and over the ocean, such as harbor engineering, transportation by sea etc. Moreover, ocean tidal power is explored as renewable energy.A well-developed global ocean tidal numerical model could be used to reproduce and predict the tidal wave dynamics, and give the space pattern of several major tide constituents, reveal the tide's effect in the ocean dynamical process.In this paper, we make an analysis on the global discrete mesh and popular global ocean tidal models, some main results are as follows:(1) Based on fundamental theories of ocean tidal dynamics, the reasons how the ocean tides are induced are presented. Moreover, we give the general procedures of buiding a numerical ocean tidal model based on some kinds of discrete global mesh.(2) In order to overcome the pole-problem induced by grid-based numerical methods on traditional longitude-latitude grid for global atmosphere and ocean circulation models, we make an analysis of many types of global discrete mesh and the corresponding numerical methods,which are used by other authors, and gives both advantages and disadvantages of each kind of mesh. After detailed analysis and comparison, global quadrilateral mesh based on a cubed sphere is preferred.(3)Based on the cubed sphere, three different methods for generation of block-structured spherical quadrilateral mesh are presented,including equi-angular gnomonic projection, conformal mapping and Laplace smoothing method. Moreover,the comparisons about these grids' quality are also presented.(4)Based on the block-structured spherical quadrilateral mesh, in the tidal dynamical equations, three major differential operators which include divergence operator, gradient operator and Laplace operator are used to test numerical experiments. A new finite volume method is utilized to approximate these differential operators. In fact, the finite volume method can also be extended on unstructured quadrilateral grids.(5)Because grid cells suffer severe deformation in the neighborhood of North pole,South pole point, this problem could be solved by two methods: one is stereographic mapping coordinate transformation, which is commonly used in global atmosphere or ocean numerical model, the other is rotated longitude-latitude coordinate transformation. After many numerical experiments on three major differential operators mentioned above, it is concluded that the rotated longitude latitude coordinate transformation is more competitive than the stereographic mapping coordinate transformation.(6)Based on the block-structured spherical quadrilateral mesh, we build a two-dimensional tidal wave model in the global ocean. The model belongs to shallow water equations, and is solved by the above-mentioned finite volume method. The compound tidal dynamics is computed under the forcing of four major diurnal and semi-diurnal tide constituents, the co-tidal charts of tide constituents M2, S2, K1, O1 are presented. Moreover, comparisons among some other well-known global ocean tidal models are made, such as NA099b model, HAMTIDE model, K-P model,FVCOM model. It's demonstrated that the built tidal model could give the spatial distribution characteristic of several major tide constituents in the global ocean accurately to a large extent.