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On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow

机译:使用欠解析的直接数值模拟对过渡湍流进行建模:平面库埃特流的情况

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Direct numerical simulations have proven of inestimable help to our understanding of the transition to turbulence in wall-bounded flows. While the dynamics of the transition from laminar flow to turbulence via localised spots can be investigated with reasonable computing resources in the domains of limited extent, the study of the decay of turbulence in conditions approaching those in the laboratory requires the consideration of domains so wide as to exclude the recourse to fully resolved simulations. Using Gibson’s C++ code Channel-Flow, we scrutinise the effects of a controlled lowering of the numerical resolution on the decay of turbulence in-plane Couette flow at a quantitative level. We show that the number of Chebyshev polynomials describing the cross-stream dependence can be drastically decreased while preserving all the qualitative features of the solution. In particular, the oblique turbulent band regime experimentally observed in the upper part of the transitional range is extremely robust. In terms of Reynolds numbers, the resolution lowering is seen to yield a regular downward shift of the upper and lower thresholds R t and R g where the bands appear and break down. The study is illustrated with the results of two preliminary experiments.
机译:直接数值模拟已证明对理解壁垒流动中的湍流过渡具有不可估量的帮助。尽管可以在有限的范围内使用合理的计算资源来研究通过局部点从层流向湍流过渡的动力学,但是在接近实验室条件的条件下研究湍流衰减的过程需要考虑以下范围:将求助于完全解析的模拟排除在外。使用吉布森(Gibson)的C ++代码Channel-Flow,我们在定量水平上仔细研究了数值分辨率受控降低对湍流平面Couette流衰减的影响。我们表明,描述跨流依赖性的Chebyshev多项式的数量可以大大减少,同时保留了解决方案的所有定性特征。特别地,在过渡范围的上部通过实验观察到的倾斜湍流带状态非常坚固。就雷诺数而言,分辨率降低会导致出现阈值并断裂的上限和下限R t 和R g 有规律的向下移动。两项初步实验的结果说明了该研究。

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