The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number $\varepsilon \ll 1$ . Using matched asymptotics, we show that a long Kelvin wave, with $O(\varepsilon ^{-1})$ length scale and $O(\varepsilon )$ amplitude relative to quasi-geostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass that is violated in the quasi-geostrophic approximation.

中文翻译：

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沿海不平衡：大气扰动产生的海洋开尔文波

半无限海洋对穿越海岸的缓慢行进的大气扰动的响应提供了一个简单的例子，说明边界引起的近地转平衡破坏。我们在小罗斯比数下检查线性浅水模型中的这种响应 $\伐普西隆\ll 1$ . 使用匹配的渐近线，我们证明了一个长开尔文波，具有 $O(\varepsilon ^{-1})$ 长度尺度和 $O(\伐普西隆)$ 当扰动穿过海岸时，会产生相对于准地转响应的幅度。考虑到这个开尔文波恢复了在准地转近似中被违反的质量守恒。