Latrache Noureddine, Mutabazi Innocent
Université de Bretagne Occidentale, IRDL/UBO UMR CNRS 6027, IUT de Brest-Morlaix, Rue de Kergoat, 29238, Brest, France.
Normandie Université, UNIHAVRE, Laboratoire Ondes et Milieux Complexes (LOMC), UMR 6294, CNRS, B.P. 540, 76058, Le Havre Cedex, France.
Eur Phys J E Soft Matter. 2021 May 2;44(5):63. doi: 10.1140/epje/s10189-021-00067-0.
Transition to inertio-elastic turbulence in Taylor-Couette flow with shear-thinning and viscoelastic polymer solutions is investigated when the rotation rate of the inner cylinder is increased and the outer cylinder is fixed. In two polymer solutions of PEO with elastic number [Formula: see text], the first instability of the circular Couette flow appears as spirals propagating in opposite directions along the axis of cylinders. Just above the onset of the spirals pattern, the localized solitons of the strong radial inflow called flame-like flow appear abruptly inside waves. The abrupt apparition of the flame-like flow is the signature of the subcritical transition to turbulence. The number of the flame-like flows follows a Gaussian distribution at given Ta number. The averaged number of the flame-like flow increases as the rotation rate is increased and it saturates in the inertio-elastic turbulence. The soliton of the strong radial inflow (flame-pattern) is created when it amplitude exceeds a critical value. The distribution of the critical amplitudes of the flame patterns follows a Gaussian law at given Ta number. The transition to turbulence is described by a mathematical model based on an error function of the probability to observe a strong inflow (flame-pattern). The statistical data of the critical amplitude and the probability to observe the flame patterns are used with the mathematical model in order to determine the stability curve of the transition to turbulence. The analysis of the transition to turbulence is completed by the characterization of the spatiotemporal properties.
当内圆柱的转速增加而外圆柱固定时，研究了在具有剪切变稀和粘弹性聚合物溶液的泰勒-库埃特流中向惯性弹性湍流的转变。在两种弹性数为[公式：见原文]的聚氧化乙烯聚合物溶液中，圆形库埃特流的首次不稳定性表现为沿圆柱轴线向相反方向传播的螺旋。就在螺旋模式开始之上，称为火焰状流的强径向流入的局部孤子在波内突然出现。火焰状流的突然出现是向湍流亚临界转变的标志。在给定的泰勒数下，火焰状流的数量遵循高斯分布。火焰状流的平均数量随着转速的增加而增加，并在惯性弹性湍流中饱和。当强径向流入的孤子（火焰模式）的振幅超过临界值时就会产生。在给定的泰勒数下，火焰模式的临界振幅分布遵循高斯定律。向湍流的转变由基于观察到强流入（火焰模式）概率的误差函数的数学模型描述。临界振幅的统计数据和观察火焰模式的概率与数学模型一起用于确定向湍流转变的稳定性曲线。通过时空特性的表征完成了对向湍流转变的分析。
