Effect of stair-step and piecewise linear topography on internal wave propagation in a geophysical flow model
Effect of stair-step and piecewise linear topography on internal wave propagation in a geophysical flow model
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阶梯和分段线性地形对地球物理流模型中内波传播的影响
DOI：
10.1029/2008jc005051
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发表时间：
2009
影响因子：
--
通讯作者：
K. Nakayama
中科院分区：
文献类型：
--
作者：
M. A. Simanjuntak;J. Imberger;K. Nakayama
[1] 本文描述了大多数数值模型中常见的底部地形阶梯表示对地球物理流中内波传播的影响。使用解析解来预测地形的阶梯和分段线性表示对内波反射和传输的影响。河口湖泊和海岸模型 (ELCOM) 用于模拟沿着包含线性分层流体的可变深度矩形通道传播的一系列小幅度内部重力波的传输。根据所得波数内容的干扰以及相关的反射系数来检查不同障碍物近似的效果，这可以直接与分析理论进行比较。结果表明，对于不同长度和高度的高斯障碍物，ELCOM 的完整底部单元和部分底部单元解分别与理论的阶梯和分段线性解一致。结果表明，当用楼梯台阶表示具有弱坡度的高斯障碍物时，会出现类似于离散傅立叶变换中的混叠现象，导致反射系数远高于精确解。另一方面，分段线性近似会产生显着衰减的混叠。与解析解类似，在实际倾斜底部强制执行无通量条件的浸没边界技术被发现不会产生更好的数值结果。
[1] The paper describes the effect of a stair-step representation of bottom topography, common in most numerical models, on the propagation of internal waves in a geophysical flow. An analytical solution was used to predict the effect of stair-step and piecewise linear representations of topography on the reflection and transmission of internal waves. The Estuary Lake and Coastal Model (ELCOM) was used to simulate the transmission of a train of small-amplitude internal gravity waves propagated along a variable depth rectangular channel containing a linearly stratified fluid. The effect of the different obstacle approximations was examined in terms of the interference of the resulting wave number content, and hence the associated reflection coefficients, which could be directly compared to the analytical theory. It was shown that for Gaussian obstacles of varying lengths and heights, the full bottom cells and partial bottom cells solutions from ELCOM agree with the stair-step and piecewise linear solutions from the theory, respectively. It was shown that when Gaussian obstacles with weak slopes are represented by stair steps, an aliasing that is similar to that in discrete Fourier transform can occur, resulting in reflection coefficients that are much higher than the exact solution. On the other hand, piecewise linear approximations produce significantly attenuated aliasing. An immersed boundary technique that enforces a no-flux condition at the actual sloping bottom, similar to that of the analytical solution, is found not to produce better numerical results.