Abstract A σ -coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method. With the selection of the low-order piecewise-constant P 0 DG and piecewise-linear P 1 DG discretisations in the vertical for the velocity and pressure fields, respectively, the proposed σ -coordinate model can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach of Zijlema and Stelling (2005), which is demonstrated through both mathematical derivation and numerical tests. Under the finite element approach, higher-order vertical discretisation choices can also be readily made which can reduce the number of vertical layers required for the accurate representation of wave dispersion. The model is verified and validated through comparisons against a series of test cases with analytical solutions or experimental measurements. All the comparisons demonstrate good agreement, indicating that the proposed model can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and can simulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is also demonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured.

中文翻译：

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一个σ坐标非静水力不连续有限元沿海海洋模型

摘要 利用非连续伽辽金有限元方法建立了σ坐标非静水静力沿海海洋模型。通过分别为速度场和压力场选择低阶分段常数 P 0 DG 和分段线性 P 1 DG 离散化，所提出的 σ 坐标模型可以自然地保留广泛的波频散特性。 - 采用 Zijlema 和 Stelling (2005) 的多层方法，通过数学推导和数值测试证明了这一点。在有限元方法下，也可以很容易地做出高阶垂直离散化选择，这可以减少准确表示波色散所需的垂直层数。该模型通过与具有分析解决方案或实验测量的一系列测试用例进行比较来验证和验证。所有的比较都证明了良好的一致性，表明所提出的模型可以准确地表示只有一层垂直层的色散正压面波，并且可以使用相对较粗的网格分辨率以合理的精度模拟斜压内波。还证明可以适当地确保正压流和斜压流耦合的一致性。并且可以使用相对较粗的网格分辨率以合理的精度模拟斜压内波。还证明可以适当地确保正压流和斜压流耦合的一致性。并且可以使用相对较粗的网格分辨率以合理的精度模拟斜压内波。还证明可以适当地确保正压流和斜压流耦合的一致性。