We have studied the transformation process from primary instabilities to secondary instabilities with direct numerical simulations and stability theories (Spatial Biglobal and plane-marching parabolized stability equations) in detail. First Mack mode and second Mack mode are shown to be able to evolve into the sinuous mode and the varicose mode of secondary instability, respectively. Although the characteristics of second Mack mode eventually lose in the downstream due to the synchronization with the continuous spectrum, second Mack mode is found to be able to trigger a sequence of mode resonations which in turn give birth to highly unstable secondary instabilities. In contrast, first Mack mode does not involve in any mode synchronization. Nevertheless, it can still “jump" to a sinuous mode of secondary instability with a much larger growth rate than that of the first Mack mode. Therefore, secondary instabilities of Görtler vortices are highly receptive to the primary instabilities in the upstream, so that one should consider the primary instability in the upstream and the secondary instability in the downstream as a whole in order to get an accurate prediction of the boundary layer transition.

中文翻译：

---

从Görtler涡流的主要不稳定性到次要不稳定性

我们已经使用直接数值模拟和稳定性理论（空间Biglobal和平面行进抛物稳定方程）详细研究了从原初不稳定性到次要不稳定性的转换过程。示出第一麦克模式和第二麦克模式分别能够发展为继发性不稳定的正弦模式和曲张模式。尽管第二个Mack模式的特性最终由于与连续频谱的同步而最终在下游丢失，但是发现第二个Mack模式能够触发一系列模式共振，进而引起高度不稳定的次级不稳定性。相反，第一个Mack模式不涉及任何模式同步。尽管如此，它仍然可以“跳跃” 到第二种不稳定的弯曲模式，其增长率比第一种Mack模式大得多。因此，Görtler涡旋的次要不稳定性高度接受上游的主要不稳定性，因此应整体考虑上游的主要不稳定性和下游的次要不稳定性，以便准确地预测边界层。过渡。