Vertical Structure of Baroclinic Instability in a Three-Layer Quasigeostrophic Model over a Sloping Bottom Journal of Physical Oceanography

We use a three-layer quasigeostrophic model to study the effects of sloping bottom topography on baroclinic instability in an ocean-like setting. Three layers allow for an interior potential vorticity gradient, a feature that is precluded by the use of a two-layer model. Material conservation of quasigeostrophic potential vorticity (QG PV) is expressed in terms of sloping background density interfaces, perturbations to the sloping interfaces, and the bottom slope. Linear stability analysis and numerical simulations of initial linear growth are used to demonstrate the dependence of topographic modifications to baroclinically unstable modes on background shear and stratification. Instabilities are classified according to their vertical structure, and the nature of topographic modification to baroclinically unstable modes is shown to correspond to instability type. Surface-intensified vertical shear of the background flow supports surface-intensified baroclinic instability that is less sensitive to bottom topography, compared to uniformly sheared background flow. When background shear is constant or close-to-constant, topography has a leading order effect on the vertical structure of the most baroclinically unstable mode. Upper-ocean stratification changes the lateral and vertical scales of the most unstable mode, with weaker upper-ocean stratification supporting high-wavenumber surface-intensified baroclinically unstable modes that are less sensitive to topography. We also present and assess a novel criterion that predicts the degree of surface intensification of the fastest-growing baroclinically unstable mode using only prescribed background properties, highlighting the role of interior potential vorticity in setting the most unstable mode’s vertical structure. Grant no. NA18OAR4320123 Grant no. NA23OAR4320198

本研究采用三层准地转模型（quasigeostrophic model），在类海洋环境下探究倾斜海底地形对斜压不稳定（baroclinic instability）的影响。三层模型能够刻画内部位涡（potential vorticity, PV）梯度这一两层模型无法实现的特征。准地转位涡（quasigeostrophic potential vorticity, QG PV）的物质守恒关系可通过倾斜背景密度界面、界面扰动及海底坡度进行表述。本研究通过线性稳定性分析与初始线性增长数值模拟，揭示了地形对斜压不稳定模态的调制作用与背景切变及层结的依赖关系。研究依据垂直结构对不稳定模态进行分类，并发现地形对斜压不稳定模态的调制特性与不稳定类型直接对应。与均匀切变的背景流场相比，表层增强型背景垂直切变所对应的表层增强型斜压不稳定对海底地形的敏感性更低。当背景切变恒定或近似恒定时，地形对最不稳定斜压模态的垂直结构具有主导阶次的影响。上层海洋层结会改变最不稳定模态的水平与垂直尺度：较弱的上层海洋层结会催生对地形敏感性更低的高波数表层增强型斜压不稳定模态。本研究还提出并评估了一项全新判据：仅通过给定的背景场参数即可预测增长最快的斜压不稳定模态的表层增强程度，同时阐明了内部位涡对最不稳定模态垂直结构的调控作用。资助编号：NA18OAR4320123、NA23OAR4320198