斜压海洋动力学的一种三维数值模式 Ⅰ.动力学方程数值格式

依据自由海面海洋动力学原始方程建立了一种三维有限差分数值模式，可用于潮波、风暴潮和海流的数值模拟和预报。运动方程和连续方程的数值格式采用内、外模态分离的技术。外模态采用交替方向隐格式，用于计算海面高度和垂直平均流速，时间步长不受Ｃｏｕｒａｎｔ－Ｆｒｉｄｅｒｉｃｈｓ－Ｌｅｗｙ条件限制；内模态采用半隐格式，用于计算海流的垂直２颁布，其时间步长可大于外模态时间步长。模式的计算程度比一般显式模式可快１０倍

A THREE-DIMENSIONAL NUMERICAL MODEL FOR BAROCLINIC OCEAN DYNAMICSI. NUMERICAL SCHEME FOR HYDRODYNAMIC EQUATIONS

This 3-D numerical model based on the primitive equations of ocean dynamics can be applied for numerical simulation and prediction of tides, storm surges and currents in a baroclinic ocean. The numerical scheme (described in Part I of this paper) for solving the equations of motion and continuity uses the internal-external mode splitting technique. The alternating direction implicit scheme is employed for the external mode computations which give the surface heights and depth-mean currents. The time step is thus not restricted by the Courant-Friedrichs-Lewy (CFL) condition for wave propagation. A semi-implicit scheme is used for the internal mode computations which give the vertical structure of the currents. But the time step is restricted by the CFL condition for advection and can be significantly longer than that of the external mode computation. As a consequence, the overall computational speed can be 10 times that of the general explicit models.

The Arakawa C-grid is adopted in the present model. In the horizontal, the spheric coordinate is adopted to facilitate large area computations. In the vertical, the grid levels are consistent with the z-coordinate. The topography is represented by a stepwise bottom. The superiority of using the z-coordinate instead of the sigma-coordinate in the vertical discretization is that it can avoid the instability in the region of steep topography and the excessive artificial diffusivity across isopycnal surfaces induced by the layout of grid points in line with the sigma-coordinate.

The computations of the external and internal modes are coupled with each other. The external mode computations are performed with a time step generally shorter than 10 times the CFL condition for wave propagation and the internal mode computations are performed with a time step shorter than the CFL condition for advection. The latter is generally longer than the former. In the external mode computations, the advection and bottom friction terms are calculated based on the internal mode results and thus the errors existing in the corresponding terms of the 2-D equations can be removed. To retain the consistency between external mode and internal mode results, the computed depth-averaged velocities of the internal mode are adjusted to be equal to the velocities of the external mode. This implies that internal mode computations only specify the vertical variations of the velocity.