Normal rossby modes of a closed basin with topography
Normal rossby modes of a closed basin with topography
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具有地形的封闭盆地的正态罗斯比模态
DOI：
10.1029/jc083ic04p01947
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发表时间：
1978
影响因子：
--
通讯作者：
P. Ripa
中科院分区：
文献类型：
--
作者：
P. Ripa
利用变分原理，提出了一种近似解析方法，用于评价带地形的旋转封闭盆地的非发散正态模态。作为一个例子，研究了大陆架、洋中脊和海山对平坦盆地模态的影响。给出了高阶模态的频率对问题参数的依赖关系；特别强调了地形的宽度和高度以及行星涡度β梯度的相对重要性。衡量这两种效应相对权重的合适参数是τ =∫ƒ2(∇ln h)2 dΛ/∫β2， dA中h为深度，f为科里奥利参数，积分在整个盆地进行。在研究的三个案例中，对于τ值大于0.25/δ的基本模态，对于具有相对宽度为δ的陆架或脊的方形盆地，以及具有海山的圆形盆地，地形效应很重要。当地形很重要时，发现结构和模态频率都与平底情况有很大的偏离。朗盖-希金斯表明，在一定深度下，模态扩展到整个盆地。最严重模态的频率约为ω = βL/2π，其中长度尺度L为盆地尺寸的数量级；高阶模态有较大的周期，累加点在零频率。在上述研究的情况下，随着τ的增加，模态倾向于被捕获在地形特征上，因此长度尺度减少到地形宽度的数量级。另一方面，在俘获区β的有效值显著增大，达到h∇(f /h)的量级。最终结果是特征频率的增加。将计算结果与数值模型的结果进行了比较，得到了适用于强地形的陆架和海脊的近似公式。
A variational principle is used to develop an approximate analytical method for the evaluation of the nondivergent normal modes of a rotating closed basin with topography. As an example, the effects of a continental shelf, a mid-ocean ridge, and a seamount on the modes of an otherwise flat basin are studied. The dependence of the frequency of the higher modes on the parameters of the problem is shown; in particular, emphasis is given to the relative importance of the width and height of the topography and the gradient of planetary vorticity β. A suitable parameter to measure the relative weight of both effects is τ = ∫∫ƒ2(∇ ln h)2 dΛ/∫∫β2, dA where h is the depth, ƒ is the Coriolis parameter, and the integration is carried over the whole basin. In the three cases studied, topographic effects are important for the fundamental mode for values of τ larger than 0.25/δ, for a square basin with a shelf or a ridge of relative width δ, and τ ∼0.5 for a circular basin with a seamount. When the topography is important, large departures from the flat bottom case are found for both the structure and the frequency of the modes. Longuet-Higgins showed that for a constant depth the modes extended over the whole basin. The frequency of the gravest mode is approximately ω = βL/2π, where the length scale L is of the order of the dimensions of the basin; higher modes have larger periods with an accumulation point at zero frequency. In the cases studied above the modes tend to be trapped over the topographic features as τ increases, and thus the length scale is reduced to something of the order of the width of the topography. But on the other hand, the effective value of β is considerably increased to the magnitude of h∇(ƒ/h) in the trapping region. The net result is an increase of the eigenfrequencies. The results are compared with those of numerical models, and approximate formulae, valid for strong topography, are developed for the shelf and ridge cases.