The results of a comparative analysis based upon a Karhunen-Lo\`{e}veexpansion of turbulent pipe flow and drag reduced turbulent pipe flow byspanwise wall oscillation are presented. The turbulent flow is generated by adirect numerical simulation at a Reynolds number $Re_\tau = 150$. The spanwisewall oscillation is imposed as a velocity boundary condition with an amplitudeof $A^+ = 20$ and a period of $T^+ = 50$. The wall oscillation results in a 27%mean velocity increase when the flow is driven by a constant pressure gradient.The peaks of the Reynolds stress and root-mean-squared velocities shift awayfrom the wall and the Karhunen-Lo\`{e}ve dimension of the turbulent attractoris reduced from 2453 to 102. The coherent vorticity structures are pushed awayfrom the wall into higher speed flow, causing an increase of their advectionspeed of 34% as determined by a normal speed locus. This increase in advectionspeed gives the propagating waves less time to interact with the roll modes.This leads to less energy transfer and a shorter lifespan of the propagatingstructures, and thus less Reynolds stress production which results in dragreduction.
展开▼
机译：给出了基于湍流管流动的Karhunen-Lo {e}膨胀和通过跨壁振动引起的阻力减小的湍流管流动的比较分析的结果。湍流通过雷诺数$ Re_ \ tau = 150 $的直接数值模拟生成。跨壁振动作为速度边界条件而施加，其振幅为$ A ^ + = 20 $，周期为$ T ^ + = 50 $。当以恒定的压力梯度驱动流动时，壁的振动导致平均速度增加27％。雷诺应力的峰值和均方根速度的峰值移离壁和Karhunen-Lo {e} ve湍流吸引器的尺寸从2453减小到102。相干的涡旋结构被推离壁而进入更高的流速，导致其平流速度增加了34％（由正常速度轨迹确定）。对流速度的增加使传播的波与滚动模式相互作用的时间更少，这导致更少的能量传递和传播结构的寿命缩短，从而减少了雷诺应力产生，从而降低了阻力。
展开▼
