A Structural Bifurcation Analysis of Flow Phenomenon for Shear Flow Past an Inclined Square Cylinder: Application to 2D Unsteady Separation

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.