On the baroclinic instability of cold-core coupled density fronts on a sloping continental shelf
On the baroclinic instability of cold-core coupled density fronts on a sloping continental shelf
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倾斜大陆架上冷核耦合密度锋的斜压不稳定性
DOI：
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发表时间：
1991
影响因子：
3.7
通讯作者：
G. Swaters
中科院分区：
文献类型：
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作者：
G. Swaters
提出了一种理论来描述倾斜大陆架上耦合密度锋的线性斜压不稳定性。用于研究不稳定过程的新斜压模型方程对应于“中等长度尺度”动态平衡。具体来说，锋面动力学虽然是地转的，但不是准地转的，因为锋面高度偏转与锋面尺度高度相比并不小。锋面高度的演变通过静水平衡与周围斜坡水中的地转压力紧密耦合，这表示了锋面界面动态压力的连续性。周围较深的斜坡水以准地转方式演化，并通过与扰动密度锋（允许释放平均锋面势能）相关的斜压涡管拉伸/压缩以及与倾斜底部相关的地形涡度梯度与锋面耦合。结果表明，斜压稳定性特征主要由所谓的无量纲相互作用参数（表示为μ）决定，该参数物理上测量不稳定斜压涡管拉伸/压缩与稳定地形涡度梯度的比率。对于给定的沿前模波数，结果表明，不稳定需要最小的 μ。提出了其他几个一般稳定性结果：不稳定的必要条件、增长率和相速度界限、高波数截止的存在以及不稳定模式的半圆定理。精确求解抛物线耦合密度前沿的线性稳定性方程，并给出不稳定性的空间和时间特征的详细描述。对于物理真实参数值，不稳定性表现为斜坡水中放大的地形罗斯贝波，而在密度前沿，不稳定扰动采取放大反气旋的形式，其在近海一侧具有最大振幅。
A theory is presented to describe the linear baroclinic instability of coupled density fronts on a sloping continental shelf. The new baroclinic model equations used to study the instability process correspond to an ‘intermediate lengthscale’ dynamical balance. Specifically, the frontal dynamics, while geostrophic, is not quasigeostrophic because frontal height deflections are not small in comparison with the frontal scale height. The evolution of the frontal height is strongly coupled to the geostrophic pressure in the surrounding slope water through the hydrostatic balance which expresses the continuity of the dynamic pressures across the frontal interface. The deeper surrounding slope water evolves quasi-geostrophically and is coupled to the front by baroclinic vortex-tube stretching/compression associated with the perturbed density front (allowing the release of mean frontal potential energy) and the topographic vorticity gradient associated with the sloping bottom. It is shown that the baroclinic stability characteristics are principally determined by a so-called non-dimensional interaction parameter (denoted μ) which physically measures the ratio of the destabilizing baroclinic vortex-tube stretching/compression to the stabilizing topographic vorticity gradient. For a given along-front mode wavenumber it is shown that a minimum μ is required for instability. Several other general stability results are presented: necessary conditions for instability, growth rate and phase speed bounds, the existence of a high wavenumber cutoff, and a semicircle theorem for the unstable modes. The linear stability equations are solved exactly for a parabolic coupled density front and a detailed description of the spatial and temporal characteristics of the instabilities is given. For physically realistic parameter values the instabilities are manifested as amplifying topographic Rossby waves in the slope water, and on the density front the unstable perturbations take the form of amplifying anticyclones which have maximum amplitude on the offshore side.