边缘不稳定Holmboe模
Marginally unstable Holmboe modes
摘要：
研究了光滑密度和速度剖面的边缘不稳定Holmboe模。对于一个大家庭的流动和分层表现出Holmboe不稳定性，我们表明，相速度等于剪切的最大或最小速度的模式是轻微的不稳定。这使我们能够确定控制参数R（表示速度变化长度尺度与密度变化长度尺度之比）的临界值，Holmboe不稳定性出现R=2。然后，我们研究系统的参数R是非常接近这个临界值。在这种情况下，我们推导出一个解析表达式的色散关系的复相速度c（k）在不稳定区域。不稳定波数区域的增长率和宽度对R偏离临界值有很强的（指数）依赖性。两个具体的例子进行了检查，并讨论了结果的影响。
英文摘要：
Marginally unstable Holmboe modes for smooth density and velocity profiles are studied. For a large family of flows and stratification that exhibit Holmboe instability, we show that the modes with phase velocity equal to the maximum or the minimum velocity of the shear are marginally unstable. This allows us to determine the critical value of the control parameter R (expressing the ratio of the velocity variation length scale to the density variation length scale) that Holmboe instability appears R=2. We then examine systems for which the parameter R is very close to this critical value. For this case we derive an analytical expression for the dispersion relation of the complex phase speed c(k) in the unstable region. The growth rate and the width of the region of unstable wave numbers has a very strong (exponential) dependence on the deviation of R from the critical value. Two specific examples are examined and the implications of the results are discussed.
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