Abstract

The classical problem of geophysical hydrodynamics is the problem of instability of a zonal geostrophic flow with a vertical velocity shear. At present, the instability with respect to symmetric perturbations that do not depend on the coordinate along the flow has been most thoroughly studied. For a symmetric instability to arise, the two-dimensional perturbation wave vector must lie inside a certain sector in the vertical plane of the wave numbers. In this paper, we study the instability with respect to unsymmetric perturbations oriented at an angle to the flow. Fundamentally new features of the temporal dynamics of the amplitudes of such perturbations are found. The main feature is associated with the existence of a stage of exponential explosive growth of finite duration. A kinematic interpretation of this stage is given that is related to the passage of the projection of the three-dimensional wave vector onto the plane transversely to the flow through the sector of symmetric instability.

中文翻译：

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垂直剪切流中不对称扰动的爆炸性增长

摘要

地球物理流体动力学的经典问题是具有垂直速度切变的纬向地转流的不稳定性问题。目前，不依赖于沿流坐标的对称扰动的不稳定性已经得到了最彻底的研究。为了出现对称不稳定性，二维扰动波矢量必须位于波数垂直平面的某个扇区内。在本文中，我们研究了与流动成一定角度的不对称扰动的不稳定性。发现了此类扰动幅度的时间动态的根本新特征。主要特征与有限持续时间的指数爆炸性增长阶段的存在有关。给出了该阶段的运动学解释，该解释与三维波矢量在横向于穿过对称不稳定区域的流动的平面上的投影的通过有关。