It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of non-rotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear stages. Distinct patterns of behaviour are found: the transient growth leading to nonlinearity at low rotation rates $Ro$, a highly chaotic intermediate $Ro$ regime, a localised weak chaos at higher $Ro$, and complete stabilization of transient disturbances at very high $Ro$. At very low $Ro$, the transient growth amplitudes are close to those for non-rotating flow, but Coriolis forces already assert themselves by producing distinct asymmetry about the channel centreline. Nonlinear processes are then triggered, in a streak-breakdown mode of transition. The high $Ro$ regimes do not show these signatures, here the leading eigenmode emerges as dominant in the early stages. Elongated structures plastered close to one wall are seen at higher rotation rates. Rotation is shown to reduce non-normality in the linear operator, in an indirect manifestation of Taylor--Proudman effects. Although the critical Reynolds for exponential growth of instabilities is known to vary a lot with rotation rate, we show that the energy critical Reynolds number is insensitive to rotation rate. It is hoped that these findings will motivate experimental verification, and examination of other rotating flows in this light.
Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor
在本研究中，进一步开发了基于平方根张量的可实现代数雷诺应力模型[Phys. Rev. E \textbf{92}，053010（2015）]，以将其适用性扩展到更复杂的流动。在传统方法中，当代数雷诺应力模型涉及平均速度梯度的高阶非线性项时，很难构造满足可实现条件的模型。预测具有三维平均速度的湍流时需要这种高阶非线性项。本文基于平方根张量的建模方法使模型始终满足可实现性条件，即使模型中包含高阶非线性项。为了构造适用于三维平均速度的湍流的代数雷诺应力模型，提出了一种四次非线性涡粘性模型。在槽道湍流、均质剪切湍流和轴向旋转管流中对模型的性能进行了数值验证。本模型对每一种湍流都给出了较好的结果。注意，由于本模型涉及立方非线性，因此再现了轴向旋转湍流管流中的平均旋流。这种高阶可实现的代数雷诺应力模型，涉及平均速度的四次非线性，预计是有用的数值稳定的预测与三维平均速度的湍流。
