The problem of the propagation of linear Rossby waves in horizontally inhomogeneous non-zonal flows is studied. The explicit solution within the geometric optics (WKBJ) approximation is found to be identical to the exact Cauchy problem solution for the case of a constant horizontal velocity shear.The effect of the short-wave transformation of Rossby waves near the so-called critical layer is detailed for the arbitrary direction of non-zonal flow. In the general case, this transformation can occur in two ways: (1) as an adhering, a monotonic approaching of wave packets to the critical layer for an infinitely long time. The sign of the intrinsic frequency of the packet remains the same all the time; (2) as an adhering with overshooting when the wave packet, first, crosses its critical layer at finite wavenumber. The wave changes the sign of the intrinsic frequency when overshooting the critical layer and then keeps the sign when it is adhering to this layer asymptotically similarly to the previous scenario. The latter regime does not exist for zonal flows, that degenerates the short-wave dynamics of Rossby waves in this special case. On the contrary, the anisotropy of the dispersion relation permits both positive and negative frequencies in a non-zonal flow. It allows for the effective use of the concept of waves of negative energy for the analysis of the stability of large-scale currents.

中文翻译：

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非纬向流上的罗斯比波：临界层效应的结构稳定性

研究了线性Rossby波在水平非均匀非纬向流动中的传播问题。发现几何光学 (WKBJ) 近似内的显式解与水平速度恒定剪切情况下的精确柯西问题解相同。 所谓临界层附近罗斯比波的短波变换的影响详细说明了非区域流的任意方向。在一般情况下，这种转换可以通过两种方式发生：（1）作为一种粘附，波包在无限长的时间内单调接近临界层。数据包固有频率的符号始终保持不变；(2) 当波包首先以有限波数穿过其临界层时，作为具有超调的粘附。波在超过临界层时改变固有频率的符号，然后在附着在该层上时保持符号，与前一场景类似。后一种状态对于纬向流不存在，在这种特殊情况下，它退化了罗斯比波的短波动力学。相反，色散关系的各向异性允许非带状流中的正频率和负频率。它允许有效地利用负能量波的概念来分析大尺度电流的稳定性。在这种特殊情况下，这使罗斯比波的短波动力学退化。相反，色散关系的各向异性允许非带状流中的正频率和负频率。它允许有效地利用负能量波的概念来分析大尺度电流的稳定性。在这种特殊情况下，这使罗斯比波的短波动力学退化。相反，色散关系的各向异性允许非带状流中的正频率和负频率。它允许有效地利用负能量波的概念来分析大尺度电流的稳定性。