Jun Yonggun, Steinberg Victor
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056325. doi: 10.1103/PhysRevE.84.056325. Epub 2011 Nov 28.
We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.
我们报告了在高分子量聚丙烯酰胺的稀聚合物溶液于高粘度水 - 糖溶剂中形成的曲线形通道流中弹性湍流的详细定量研究。对平均速度、均方根速度以及速度梯度剖面的详细研究揭示了与通道内弹性应力非均匀分布相关的边界层的出现。特征边界宽度与魏森贝格数Wi无关，且与通道宽度成正比，这与我们早期在不同流动几何形状中对弹性湍流边界层的研究结果一致。通道内弹性应力的非均匀分布以及主体流中速度和速度梯度相关函数中速度和速度梯度的特征空间尺度（其量级为边界层宽度）的出现，可能表明集中在边界层的过大弹性应力会像最近在弹性湍流中被动标量混合中观察到的射流那样被喷射到主体流中。最后，实验结果表明，尽管弹性湍流理论很好地解释了所观察到的速度功率谱的尖锐幂律衰减，但该理论的一个主要预测，即在弹性湍流主体流中归一化均方根速度梯度的饱和，在定性和定量上都与实验观测结果相矛盾。这些实验结果要求进一步发展有界容器中弹性湍流的理论，类似于对被动标量问题所做的那样。
