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Stability analysis of shear-thinning flow between rotating cylinders

机译：旋转圆柱体间稀疏流的稳定性分析

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Stability of the shear thinning Taylor-Couette flow is carried out and complete bifurcation diagram is drawn. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed, that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.
机译：进行了剪切稀化泰勒-库特流的稳定性，并绘制了完整的分叉图。假定流体遵循Carreau-Bird模型并施加混合边界条件。由质量和动量方程守恒的Galerkin投影得出的低阶动力学系统，在速度分量中还包括其他非线性项，这些非线性项源自于与剪切有关的粘度。可以看出，随着剪切稀化效果的增加，基本流在较低的临界泰勒数下失去了对旋涡结构的径向流稳定性。涡流的出现对应于超临界分叉的开始，这在线性流体的流动中也可以看到。但是，与牛顿情况不同，当泰勒数达到与霍夫夫分叉的开始相对应的第二临界数时，剪切稀疏的泰勒涡旋失去了稳定性。分叉图中针对不同情况给出了完整的流场以及粘度图。

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