定量地将Eady模型映射到双层准地转模型
Quantitatively mapping the Eady model onto a two-layer quasi-geostrophic model
AI总结：
本文通过定量映射Eady模型与双层准地转模型，揭示了在弱底摩擦条件下，利用2LQG模型的扩散率预测Eady模型的涡旋扩散率的方法。
摘要：
双层准地转模型（2LQG）和Eady模型是两个理想化的系统，用于说明大气喷流和海洋环流的次级环流不稳定性。这两个设置有许多共同的要素——快速旋转框架中密度分层流体的垂直剪切背景流——但复杂性和维度上有所不同。Eady模型具有连续的垂直方向，其次级环流湍流由上下边界位势涡度（PV）梯度引起。相比之下，2LQG系统通常通过内部PV梯度来建模次级环流不稳定性。这种区别挑战了我们清晰识别通过更简单的2LQG系统推导出Eady动态的两种'模式'的能力。在本研究中，我们表明在弱底摩擦引起的湍流状态下，这一困难可以被克服。具体而言，通过两者都组织成涡旋气体的共同结构，我们确定了Eady模型与2LQG模型之间的定量映射。这种映射允许在了解2LQG扩散率的情况下，无需参数即可预测Eady模型的涡旋扩散率。我们通过线性或二次底摩擦的Eady和2LQG模型的数值模拟来说明这些结果。
英文摘要：
The two-layer quasigeostrophic model (2LQG) and the Eady model are two idealized systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two setups share many ingredients -- background vertically sheared zonal flow of density-stratified fluid in a rapidly rotating frame -- while differing in complexity and dimensionality. The Eady model has a continuous vertical direction, with baroclinic turbulence induced by boundary potential vorticity (PV) gradients at top and bottom. By contrast, the 2LQG sytem typically models baroclinic instability induced by interior PV gradients. This distinction challenges our ability to clearly identify a couple of 'modes' through which the Eady dynamics could be inferred from a simpler 2LQG system. In the present study, we show that this difficulty can be circumvented in the turbulent regime arising for weak bottom drag. Namely, guided by the common organization of both systems into a gas of coherent vortices, we identify a quantitative mapping between the Eady and the 2LQG models. The mapping allows for parameter-free predictions of the eddy diffusivity of the Eady model based on the knowledge of the 2LQG diffusivity. We illustrate these results using numerical simulations of the Eady and 2LQG models with linear or quadratic bottom drag.
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