Abstract

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 \(E \in \left\{ 0.16 ; 0.30 \right\} \), 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.

Graphic Abstract

中文翻译：

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通过粘弹性泰勒-库埃特流中的火焰模式过渡到湍流

摘要

当内圆柱的旋转速率增加而外圆柱固定时，利用剪切稀化和粘弹性聚合物溶液，研究了泰勒-库埃特流向惰性弹性湍流的过渡。在两个具有弹性数\（E \ in \ left \ {0.16; 0.30 \ right \} \）的PEO聚合物溶液中，圆形Couette流的第一个不稳定性表现为沿圆柱体轴线在相反方向上传播的螺旋。刚好在螺旋形波的开始上方，强烈的径向流（称为火焰状流）的局部孤子突然出现在波内。火焰状流动的突然消失是亚临界过渡到湍流的标志。在给定的Ta数下，火焰状流的数量遵循高斯分布。随着转速的增加，火焰状流动的平均数量增加，并且在惰性弹性湍流中达到饱和。当振幅超过临界值时，将产生强烈的径向流入孤子（火焰模式）。火焰图案的临界振幅的分布在给定的Ta数下遵循高斯定律。由数学模型描述了湍流的过渡，该数学模型基于观察到强流入（火焰模式）的概率的误差函数。临界振幅的统计数据和观察火焰模式的可能性与数学模型一起使用，以便确定湍流过渡的稳定性曲线。向湍流过渡的分析通过时空特性的表征完成。

图形摘要