论文标题
阈值瞬态生长作为湍流平均轮廓的标准
Threshold transient growth as a criterion for turbulent mean profiles
论文作者
论文摘要
Lozano-Duran et al (J. Fluid Mech., 914, A8, 2021) have recently identified the ability of streamwise-averaged turbulent streak fields $U(y,z,t)\widehat{\mathbf{x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_τ=180$.在这里，为了将此结果扩展到较大的域和更高的$re_τ$，我们通过首先选择预期在动荡的平均值$ u（y）\ wideHat {\ nathbf {x x} $上的涡流概况$ u（y）上的涡流周转时间出现的主要条纹结构，将其建模为两阶段的线性过程。 $ u（y，z）\ wideHat {\ mathbf {x}} $。选择平均条纹振幅和与模拟一致的涡流周转时间捕获了Lozano-Duran等人发现的生长阈值。 （2021）用于持续的湍流。在$re_τ= 180 $的较大域中，在模拟中观察到的最有力的近壁条纹接近预测的最佳条纹。这种最有活力的条纹间距接近$re_τ= 550 $的最佳条纹，在每个$中，每个二次增长也可能融合在一起。该模型的关键预测是，维持湍流所需的阈值瞬态增长会随着$re_τ$的增加而降低。从根本上讲，Lozano-Duran等人的工作。 （2021），我们的结果表明，关于Malkus的（J. Fluid Mech。}，521，1，1956）的经典假设是微妙但显着的修改。可实现的湍流平均轮廓的关键特性可能是能够产生足够的短期瞬态增长，而不是依赖其（长期）线性稳定性特征，这是Malkus的最初想法。
Lozano-Duran et al (J. Fluid Mech., 914, A8, 2021) have recently identified the ability of streamwise-averaged turbulent streak fields $U(y,z,t)\widehat{\mathbf{x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_τ=180$. Here, in an attempt to extend this result to larger domains and higher $Re_τ$, we model this streak transient growth as a two-stage linear process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile $U(y)\widehat{\mathbf{x}}$, and then examining the secondary growth on this (frozen) streak field $U(y,z)\widehat{\mathbf{x}}$. Choosing the mean streak amplitude and eddy turnover time consistent with simulations captures the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. In a larger domain at $Re_τ=180$, the most energetic near-wall streaks observed in simulations are close to the predicted optimal streaks. This most energetic streak spacing, approaches the optimal streak at $Re_τ=550$ where the secondary growth possible on each also comes together. A key prediction from the model is that the threshold transient growth required to sustain turbulence decreases with increasing $Re_τ$. More fundamentally, the work of Lozano-Duran et al. (2021) and our results suggest a subtle but significant revision of Malkus's (J. Fluid Mech.}, 521, 1, 1956) classic hypothesis concerning realisable turbulent mean profiles. The key property for a realisable turbulent mean profile could be the ability to generate sufficient short-term transient growth rather than dependence on its (long-term) linear stability characteristics which was Malkus's original idea.
