The aim of this study is to understand the dynamics of Rossby waves induced by a localised and periodic ‘plunger’ forcing – imposed on a background flow – which is intended as an elementary representation of transient mesoscale eddy forcing in the ocean. We consider linearised dynamics and its quasi-nonlinear extension, and focus on the rotating shallow-water model. The plunger induces a spectrum of Rossby waves that drive zonal momentum flux convergence at the forced latitudes. This behaviour has a robust and significant dependence on the background flow, which we treat as zonal and uniform. We systematically analyse this dependence using two methods. First, we use the eddy geometry formulation, in which Reynolds stresses are expressed in terms of eddy elongation and eddy tilt parameters, and consider the relationship between eddy geometry and zonal momentum redistribution. Second, we implement decompositions of flow responses into linear dynamical eigenmodes and compare with expectations from linear Rossby wave theory. Both methods compliment each other and aid the understanding of zonal momentum redistribution and its dependence on uniform background flow. We find that this dependence is determined by two factors: (i) dispersion-constrained resonance with the plunger forcing and (ii) efficiency of nonlinear eddy self-interactions. These results significantly improve our understanding of shallow-water Rossby waves, and may also be applied towards the development of parameterisations of oceanic mesoscale eddies.

中文翻译：

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旋转浅水模型中局部强迫引起的罗斯贝波和纬向动量重新分布

本研究的目的是了解由局部和周期性“柱塞”强迫（强加在背景流上）引起的罗斯比波的动力学，这旨在作为海洋中瞬态中尺度涡旋强迫的基本表示。我们考虑线性化动力学及其准非线性扩展，并专注于旋转浅水模型。柱塞会产生一系列罗斯比波，驱动纬向动量通量会聚在受迫纬度。这种行为对背景流具有强大且显着的依赖性，我们将其视为带状和均匀的。我们使用两种方法系统地分析这种依赖性。首先，我们使用涡流几何公式，其中雷诺应力用涡流伸长率和涡流倾斜参数表示，并考虑涡旋几何与纬向动量重新分布之间的关系。其次，我们将流动响应分解为线性动力学特征模态，并与线性罗斯比波理论的预期进行比较。这两种方法相辅相成，有助于理解纬向动量重新分布及其对均匀背景流的依赖。我们发现这种依赖性由两个因素决定：（i）与柱塞强迫的色散约束共振和（ii）非线性涡流自相互作用的效率。这些结果显着提高了我们对浅水罗斯比波的理解，也可用于海洋中尺度涡旋参数化的发展。我们将流动响应分解为线性动力学特征模态，并与线性罗斯比波理论的期望值进行比较。这两种方法相辅相成，有助于理解纬向动量重新分布及其对均匀背景流的依赖。我们发现这种依赖性由两个因素决定：（i）与柱塞强迫的色散约束共振和（ii）非线性涡流自相互作用的效率。这些结果显着提高了我们对浅水罗斯比波的理解，也可用于海洋中尺度涡旋参数化的发展。我们将流动响应分解为线性动力学特征模态，并与线性罗斯比波理论的期望值进行比较。这两种方法相辅相成，有助于理解纬向动量重新分布及其对均匀背景流的依赖。我们发现这种依赖性由两个因素决定：（i）与柱塞强迫的色散约束共振和（ii）非线性涡流自相互作用的效率。这些结果显着提高了我们对浅水罗斯比波的理解，也可用于海洋中尺度涡旋参数化的发展。我们发现这种依赖性由两个因素决定：（i）与柱塞强迫的色散约束共振和（ii）非线性涡流自相互作用的效率。这些结果显着提高了我们对浅水罗斯比波的理解，也可用于海洋中尺度涡旋参数化的发展。我们发现这种依赖性由两个因素决定：（i）与柱塞强迫的色散约束共振和（ii）非线性涡流自相互作用的效率。这些结果显着提高了我们对浅水罗斯比波的理解，也可用于海洋中尺度涡旋参数化的发展。