无粘剪切不稳定性的一个充分条件：障碍定理及其在交替急流中的应用
A sufficient condition for inviscid shear instability: Hurdle theorem and its application to alternating jets
AI总结：
提出一种识别无粘单向剪切流不稳定参数区域的简单方法，发现倒数Rossby Mach数超阈值即不稳定，改进了木星和土星急流稳定维持的理论框架。
摘要：
我们提出了一种简单的方法，用于识别一般无粘单向剪切流稳定性问题中的不稳定参数区域。该理论适用于广泛的基本流，包括非单调流。我们使用基于准地转方程的木星交替急流模型对该方法进行了说明。主要结果是：如果流动域中存在一个区间，使得倒数Rossby Mach数（一个根据纬向流和位涡分布定义的量）超过某个阈值或“障碍”，则该流动是不稳定的。当我们可以将障碍宽度设定为远大于大气的固有变形长度时（正如气态巨行星上的情况），障碍高度趋近于1。在这种情况下，Kelvin-Arnol'd稳定性充分条件能够准确检测不稳定性。这些结果改进了用于解释木星和土星急流在十年时间尺度上稳定维持的理论框架。
英文摘要：
We propose a simple method to identify unstable parameter regions in general inviscid unidirectional shear flow stability problems. The theory is applicable to a wide range of basic flows, including those that are non-monotonic. We illustrate the method using a model of Jupiter's alternating jet streams based on the quasi-geostrophic equation. The main result is that the flow is unstable if there is an interval in the flow domain for which the reciprocal Rossby Mach number (a quantity defined in terms of the zonal flow and potential vorticity distribution), surpasses a certain threshold or `hurdle'. The hurdle height approaches unity when we can take the hurdle width to greatly exceeds the atmosphere's intrinsic deformation length, as holds on gas giants. In this case, the Kelvin-Arnol'd sufficient condition of stability accurately detects instability. These results improve the theoretical framework for explaining the stable maintenance of Jupiter and Saturn's jets over decadal timescales.
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