压力梯度作用下槽道流动的统计估计
Statistical Estimates For Channel Flows Driven By A Pressure Gradient
摘要：
我们提出了严格的估计有关的一些物理量的湍流和非湍流槽道流驱动的均匀压力梯度。这样的结果是基于平稳的统计解决方案，这是有关的概念，系综平均流量统计平衡的概念。我们提供了一个下限估计的平均表面摩擦系数和改进以前的上限估计相同的数量，这两个估计的雷诺数。我们还提出了下限和上限估计的平均速率的能量耗散，平均纵向速度（在压力梯度的方向），和平均动能。特别是，我们获得了与能量耗散定律相关的上限，即平均能量耗散率本质上受无因次普适常数乘以特征宏观尺度长度上平均纵向速度的立方的限制。最后，我们调查的规模由规模的能量注入由于压力梯度，证明了上限估计的减少，这种能量注入的尺度长度减少。
英文摘要：
We present rigorous estimates for some physical quantities related to turbulent and non-turbulent channel flows driven by a uniform pressure gradient. Such results are based on the concept of stationary statistical solution, which is related to the notion of ensemble average for flows in statistical equilibrium. We provide a lower bound estimate for the mean skin friction coefficient and improve on a previous upper bound estimate for the same quantity; both estimates in terms of the Reynolds number. We also present lower and upper bound estimates for the mean rate of energy dissipation, the mean longitudinal velocity (in the direction of the pressure gradient), and the mean kinetic energy. In particular, we obtain an upper bound related to the energy dissipation law, namely that the mean rate of energy dissipation is essentially bounded by a non-dimensional universal constant times the cube of the mean longitudinal velocity over a characteristic macro-scale length. Finally, we investigate the scale-by-scale energy injection due to the pressure gradient, proving an upper bound estimate for the decrease of this energy injection as the scale length decreases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
