论文标题
在旋转环境中，法拉第不稳定性的发作和饱和
The onset and saturation of the Faraday instability in miscible fluids in a rotating environment
论文作者
论文摘要
我们使用理论模型和直接数值模拟（DNS）研究了旋转对法拉第不稳定性发作和饱和的影响。我们的分析方法利用Floquet分析来解决从线性稳定性分析获得的一组MATHIEU方程。 MATHIEU方程的解包含三维稳定图中的稳定和谐波和亚谐波不稳定区域。我们发现科里奥利的力稳定了流动，并延迟了负责在较低强迫幅度下湍流混合的亚谐波不稳定的开始。但是，在较高的强迫幅度下，流量足以减轻旋转的稳定效果，并且在旋转和非旋转环境中，湍流混合区的演变相似。这些结果通过不同的科里奥利频率和迫使幅度在不同的科里奥利频率下证实。我们还观察到，对于$ \左（f/ω\右）^2 <0.25 $，其中$ f $是科里奥利的频率，$ω$是强迫频率，不稳定性和湍流混合区尺寸-L $ $ $饱和。当$ \ left（f/ω\右）^2 \ geq0.25 $时，湍流混合区尺寸-$ l $永远不会饱和并继续增长。
We investigate the influence of rotation on the onset and saturation of the Faraday instability in a vertically oscillating two-layer miscible fluid using a theoretical model and direct numerical simulations (DNS). Our analytical approach utilizes the Floquet analysis to solve a set of the Mathieu equations obtained from the linear stability analysis. The solution of the Mathieu equations comprises stable and harmonic, and sub-harmonic unstable regions in a three-dimensional stability diagram. We find that the Coriolis force stabilizes the flow and delays the onset of the sub-harmonic instability responsible for turbulent mixing at lower forcing amplitudes. However, at higher forcing amplitudes, the flow is energetic enough to mitigate the stabilizing effect of rotation, and the evolution of the turbulent mixing zone is similar in both rotating and non-rotating environments. These results are corroborated by DNS at different Coriolis frequencies and forcing amplitudes. We also observe that for $\left(f/ω\right)^2<0.25$, where $f$ is the Coriolis frequency, and $ω$ is the forcing frequency, the instability, and the turbulent mixing zone size-$L$ saturates. When $\left(f/ω\right)^2\geq0.25$, the turbulent mixing zone size-$L$ never saturates and continues to grow.
