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Planetary, inertia–gravity and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-05-20 , DOI: 10.1002/qj.4107 Yair De-Leon 1 , Itzhak Fouxon 1 , Chaim I Garfinkel 1 , Nathan Paldor 1
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-05-20 , DOI: 10.1002/qj.4107 Yair De-Leon 1 , Itzhak Fouxon 1 , Chaim I Garfinkel 1 , Nathan Paldor 1
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A linear wave theory of the Rotating Shallow-Water Equations (RSWE) is developed in a channel on the midlatitude f-plane or -plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. Here we show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the -effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting Rossby, Poincaré and “Kelvin-like” waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure is often trapped near one of the channel's boundaries and does not oscillate across the channel. A comparison between the phase speeds of Rossby waves of the present theory and those of the Quasi-Geostrophic Shallow-Water (QG-SW) theory shows that the former can be 2.5 times faster than those of the QG-SW theory. The phase speed of “Kelvin-like” waves is modified by the presence of a mean flow compared to the classical gravity wave speed, and furthermore their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wave number, and the convexity of the dispersion curves also changes with the zonal wave number. These results have implications for the propagation of Rossby wave packets: QG theory overestimates the zonal group velocity.
中文翻译：
在存在均匀纬向流的情况下，f 平面和 β 平面上的行星、惯性重力和开尔文波
旋转浅水方程 (RSWE) 的线性波理论在中纬度f平面上的通道中发展-在存在均匀平均纬向流的情况下，该平面通过流体表面高度的经向梯度在地转上达到平衡。在这里，我们表明这个表面高度梯度是一个势涡度 (PV) 源，即使在f平面上也会产生罗斯贝波，类似于 PV 源产生这些波，例如-效应，平均流量和底部地形的剪切。RSWE 的数值解表明，由此产生的 Rossby、Poincaré 和“类开尔文”波与它们的对应物不同，它们的相速度和经向结构均没有平均流。“无平均流”相速度的多普勒频移不考虑相速度的差异，并且经向结构通常被困在通道边界之一附近并且不会在通道上振荡。本理论与准地转浅水（QG-SW）理论的Rossby波相速度比较表明，前者可以比QG-SW理论快2.5倍。与经典重力波速度相比，“类开尔文”波的相速度因平均流的存在而改变，而且它们的经向速度不会消失。相邻庞加莱模式的色散曲线之间的间隙并不均匀，而是随着纬向波数的变化而变化，色散曲线的凸度也随着纬向波数的变化而变化。这些结果对罗斯比波包的传播有影响：QG 理论高估了纬向群速度。
更新日期：2021-05-20
中文翻译：
在存在均匀纬向流的情况下，f 平面和 β 平面上的行星、惯性重力和开尔文波
旋转浅水方程 (RSWE) 的线性波理论在中纬度f平面上的通道中发展-在存在均匀平均纬向流的情况下，该平面通过流体表面高度的经向梯度在地转上达到平衡。在这里，我们表明这个表面高度梯度是一个势涡度 (PV) 源，即使在f平面上也会产生罗斯贝波，类似于 PV 源产生这些波，例如-效应，平均流量和底部地形的剪切。RSWE 的数值解表明，由此产生的 Rossby、Poincaré 和“类开尔文”波与它们的对应物不同，它们的相速度和经向结构均没有平均流。“无平均流”相速度的多普勒频移不考虑相速度的差异，并且经向结构通常被困在通道边界之一附近并且不会在通道上振荡。本理论与准地转浅水（QG-SW）理论的Rossby波相速度比较表明，前者可以比QG-SW理论快2.5倍。与经典重力波速度相比，“类开尔文”波的相速度因平均流的存在而改变，而且它们的经向速度不会消失。相邻庞加莱模式的色散曲线之间的间隙并不均匀，而是随着纬向波数的变化而变化，色散曲线的凸度也随着纬向波数的变化而变化。这些结果对罗斯比波包的传播有影响：QG 理论高估了纬向群速度。
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