Secondary optimal energy growth and magnetic damping of turbulence in Hartmann channel flow
Secondary optimal energy growth and magnetic damping of turbulence in Hartmann channel flow
复制标题
哈特曼通道流中湍流的二次最优能量增长和磁阻尼
DOI：
10.1016/j.euromechflu.2016.06.008
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发表时间：
2016-11-01
影响因子：
2.6
通讯作者：
Boeck, Thomas
中科院分区：
文献类型：
--
作者：
Dong, Shuai;Krasnov, Dmitry;Boeck, Thomas
研究了哈特曼槽道流中二次线性扰动的瞬态放大。通过迭代求解直接控制方程和伴随控制方程，计算了反对称和对称条纹基流上的最优线性增长，结果表明，在较大的Hartmann数下，Hartmann层顶底之间仍存在残余相互作用。强烈放大的二次扰动时，观察到由于调制哈特曼通道流的曲折不稳定性的主要扰动有一个足够大的振幅。二次扰动的特征流向波长是有限的，并且与哈特曼层的厚度成比例。对于条纹对基流的弱调制，二次扰动是流向独立涡，类似于主最佳扰动。磁场的影响是检查通过微扰能量收支，焦耳耗散原来是弱的粘性耗散相比。因此，二次不稳定性类似于渐近吸力边界层的不稳定性。只有对于平均速度分布，洛伦兹力才是决定性的。磁场对Hartmann层内动力学的微弱影响通过附加的直接数值模拟来验证，其中Lorentz力仅考虑在平均流向动量方程中。计算结果与完全模拟的湍流Hartmann流接近，且随着Reynolds数R的增加，两者的差异减小。(C)2016 Elsevier Masson SAS。All rights reserved.
The transient amplification of secondary linear perturbations in Hartmann channel flow is investigated. Optimal linear growth on either antisymmetric or symmetric streaky base flow is calculated by iteratively solving the direct and adjoint governing equations, The result shows that there is still residual interaction between the top and bottom Hartmann layer at relatively large Hartmann number. Strong amplification of secondary perturbations due to inflectional instability of modulated Hartmann channel flow is observed when the primary perturbations have a sufficiently large amplitude. The characteristic streamwise wavelength of the secondary perturbation is finite and scales with the thickness of the Hartmann layer. For weak modulation of the basic flow by the streaks, the secondary perturbations are streamwise independent vortices that resemble the primary optimal perturbations. The influence of the magnetic field is examined by means of the perturbation energy budgets, and the Joule dissipation turns out to be weak compared with the viscous dissipation. The secondary instability is therefore similar to that of an asymptotic suction boundary layer. Only for the mean velocity profile the Lorentz force is decisive. The weak influence of the magnetic field on the dynamics within Hartmann layer is verified by additional direct numerical simulations where the Lorentz force is only taken into account in the mean streamwise momentum equation. The results are close to full simulations of turbulent Hartmann flow, and the differences reduce with growing Reynolds number R based on the Hartmann layer thickness. (C) 2016 Elsevier Masson SAS. All rights reserved.