海面浮力梯度对海洋罗斯贝波传播的影响
The effect of surface buoyancy gradients on oceanic Rossby wave propagation
摘要：
基于卫星观测到的相干西向传播地物与罗斯贝波理论之间的差异，本文重新讨论了行星波传播问题，并考虑了海洋表面横向浮力梯度的影响。长斜压Rossby波的标准理论是基于准地转拉伸算子在正常模式下的展开式$ϕ_n(z)$，满足地面上的Neumann边界条件$ϕ_n'(0) = 0$。浮力梯度，热风平衡，成比例的流函数的垂直导数，因此，这种模式是无法代表无处不在的横向浮力梯度在海洋的混合层。在这里，我们重新推导的波传播问题的扩展在最近开发的"表面感知"（SA）的基础上，可以占在海洋表面的浮力异常。这个问题是在一个理想化的Charney斜压波问题集在海洋的背景下，在那里的表面平均浮力梯度相互作用的恒定的内部位涡梯度，结果从$β$和平均切变的曲率的上下文中研究。的波频，增长率和相位进行系统的比较，从一个两层模型，截断扩展标准斜压模式和高垂直分辨率计算，代表真正的解决方案。当存在侧表面梯度时，完整解通常显示更快的波传播。此外，SA基中的波问题最好地捕获了完整的解，即使只有两个或三个模式。
英文摘要：
Motivated by the discrepancy between satellite observations of coherent westward propagating surface features and Rossby wave theory, this paper revisits the planetary wave propagation problem, taking into account the effects of lateral buoyancy gradients at the ocean's surface. The standard theory for long baroclinic Rossby waves is based on an expansion of the quasigeostrophic stretching operator in normal modes, $ϕ_n(z)$, satisfying a Neumann boundary condition at the surface, $ϕ_n'(0) = 0$. Buoyancy gradients are, by thermal wind balance, proportional to the vertical derivative of the streamfunction, thus such modes are unable to represent ubiquitous lateral buoyancy gradients in the ocean's mixed layer. Here, we re-derive the wave propagation problem in terms of an expansion in a recently-developed "surface-aware" (SA) basis that can account for buoyancy anomalies at the ocean's surface. The problem is studied in the context of an idealized Charney-like baroclinic wave problem set in an oceanic context, where a surface mean buoyancy gradient interacts with a constant interior potential vorticity gradient that results from both $β$ and the curvature of the mean shear. The wave frequencies, growth rates and phases are systematically compared to those computed from a two-layer model, a truncated expansion in standard baroclinic modes and to a high-vertical resolution calculation that represents the true solution. The full solution generally shows faster wave propagation when lateral surface gradients are present. Moreover, the wave problem in the SA basis best captures the full solution, even with just a two or three modes.
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