Abstract A structural bifurcation analysis of an incompressible two-dimensional (2D) shear flow past an inclined square cylinder by considering topological properties of flow is done in this paper. We have shown how the flow separation leads to complex structure at a time from a point by using this analysis. The streamfunction–vorticity ( $$\Psi $$ − $$\zeta $$ ) formulation of Navier–Stokes (N–S) equations in Cartesian coordinates is solved using a higher order compact (HOC) finite difference scheme. Through this analysis, we capture the exact locations of first and second bifurcation points with appropriate non-dimensional time of their occurrences for initial stages as well as fully developed flow. The flow field is mainly influenced by Reynolds number, Re, and shear rate, $$\kappa $$ . It is shown that the first and second bifurcations developed within a very small time difference from the upper and lower downstream edges of the cylinder up to $$\kappa $$ = 0.1. Numerical simulations are carried out for Re = 100, 185 with $$\kappa $$ values range from 0 to 0.4. The purpose of the present study is to elaborate on the influence of shear parameter on flow properties. The temporal behavior of vortex formation and relevant streakline patterns are scrutinized for all parameter values. Occurrence of multiple separations is demonstrated in detail by varying $$\kappa $$ for both initial and fully developed flows. Comparisons with previous results in the literature clearly verify the accuracy and validity of the present work.

中文翻译：

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斜方圆柱剪切流流动现象的结构分岔分析：在二维非定常分离中的应用

摘要 本文通过考虑流动的拓扑特性，对通过倾斜方圆柱体的不可压缩二维（2D）剪切流进行了结构分岔分析。我们已经通过使用这种分析展示了流动分离如何从一个点一次导致复杂的结构。Navier-Stokes (N-S) 方程在笛卡尔坐标系中的流函数 - 涡度 ( $$\Psi $$ − $$\zeta $$ ) 公式使用高阶紧致 (HOC) 有限差分格式求解。通过这种分析，我们捕获了第一和第二分叉点的确切位置，以及它们在初始阶段以及完全发展的流动中出现的适当无量纲时间。流场主要受雷诺数 Re 和剪切速率 $$\kappa $$ 的影响。结果表明，从圆柱体的上下下游边缘到 $$\kappa $$ = 0.1，第一和第二分叉在非常小的时间差内发展。对 Re = 100、185 进行数值模拟，$$\kappa $$ 的值范围为 0 到 0.4。本研究的目的是详细阐述剪切参数对流动特性的影响。涡旋形成的时间行为和相关的条纹图案都经过仔细检查所有参数值。通过改变初始流和完全发展流的 $$\kappa $$ 来详细证明多次分离的发生。与文献中先前结果的比较清楚地验证了当前工作的准确性和有效性。