NONLINEAR ADVECTION SCHEMES AND ENERGY CASCADE ON SEMI-STAGGERED GRIDS
NONLINEAR ADVECTION SCHEMES AND ENERGY CASCADE ON SEMI-STAGGERED GRIDS
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DOI：
10.1175/1520-0493(1984)112
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发表时间：
1984-01-01
影响因子：
3.2
通讯作者：
JANJIC, ZI
中科院分区：
文献类型：
--
作者：
JANJIC, ZI
非线性平流方案的一个常见问题是在最小可分辨尺度上能量的虚假积累。为了控制这一过程，在Arakawa（1966）之后，设计了许多交错和半交错网格的能量和涡度拟能守恒格式。本文论证了与交错网格相反，半交错网格上的能量守恒和涡度拟能并不能保证有效地限制能量从大尺度到小尺度的错误输运，采用一种新的方法来应用荒川雅可比矩阵本文首次给出了一种精确反映Arakawa无辐散流理论的半交错网格格式。这是通过交错网格上定义的能量守恒和涡度拟能来实现的。这两个量的精度较高，不能直接从半交错网格上的因变量计算。在交错网格和半交错网格上，本文所提出的格式和半交错网格上定义的能量守恒和涡度拟能守恒格式的实验结果表明，在长尺度上，本文所提出的格式和半交错网格上定义的能量守恒和涡度拟能守恒格式的能量守恒和涡度拟能守恒都有明显的差别。项积分，这是符合理论，并证明了新方案的优点。
A common problem with nonlinear advection schemes is the false accumulation of energy at the smallest resolvable scales. To keep this process under control, following Arakawa (1966), a number of energy and enstrophy conserving schemes for staggered and semi-staggered grids have been designed. In this paper, it is demonstrated that, in contrast to the staggered grid, the conservation of energy and enstrophy on the semi-staggered gods does not guarantee that the erroneous transport of energy from large to small scales will be effectively restricted.Using a new approach to the application of the Arakawa Jacobian, a scheme for a semi-staggered grid which exactly reflects the Arakawa theory for nondivergent flow is obtained for the first time. This is achieved by conservation of energy and enstrophy as defined on the staggered grid. These two quantities are of higher accuracy and cannot be calculated directly from the dependent variables on the semi-staggered grid. It is further demonstrated that the amount of energy which can be transported toward smaller scales is more restricted than for any other scheme of this type on both staggered and semi-staggered grid.Experiments performed with the proposed scheme and a scheme which conserves energy and enstrophy as defined on the semi-staggered grid reveal visible differences in long-term integrations which are in agreement with the theory and demonstrate the advantages of the new scheme.