Carpenter Peter W, Kudar Karen L, Ali Reza, Sen Pradeep K, Davies Christopher
School of Engineering, University of Warwick, Coventry CV4 7AL, UK.
Philos Trans A Math Phys Eng Sci. 2007 Oct 15;365(1859):2419-41. doi: 10.1098/rsta.2007.2016.
We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.
我们基于与克莱班诺夫模态的类比，提出了一个相对简单、确定性的湍流边界层子层条纹理论模型。我们的方法是通过虚拟体力形式的涡度源来生成缓冲层中发现的流向涡旋。结果发现，最强的条纹对应于一个展向波长，该波长处于实验观测到的统计平均条纹间距值范围内。我们还给出了结果，展示了流向压力梯度、雷诺数和壁面柔顺性对子层条纹的影响。壁面柔顺性对条纹特征影响的理论预测与实验数据吻合良好。我们还描述了为准周期猝发循环提出的理论模型，该模型将条纹建模置于背景之中。所提出的猝发过程如下：(i) 流向涡旋产生子层条纹，其他涡旋元素产生传播的平面波，(ii) 当条纹达到足够幅度时，它们与平面波非线性相互作用产生表现出瞬态增长的斜波，(iii) 斜波与平面波非线性相互作用产生流向涡旋；这些流向涡旋反过来又产生子层条纹，如此循环更新。
