Study of three-dimensional vortex shedding in the wake of a square cylinder

The objective of this study is to contribute to the understanding of the flow about rectangular cylinders by studying the low Reynolds number regime. In particular this work focuses on the transition to three-dimensionality for the flow over a square cylinder. Floquet stability analysis and direct numerical simulations of the Navier-Stokes equations are utilized to determine the regime that the flow transitions to a three-dimensional state. Also, an accurate spectral domain decomposition method has been developed and implemented on a massively parallel computer which allows for the rapid solution of the governing equations.;It is observed that three-dimensional transition process for square cylinder is similar to that of a circular cylinder. Most notably there is a long wave-length three-dimensional disturbance which becomes unstable at a Reynolds number about 170, followed by the appearance of a short wavelength instability. However, this stability analysis also predicts a intermediate wavenumber disturbance which has a shedding frequency twice that of the base flow. This intermediate wavelength mode has not been observed in analysis of the circular cylinder. The presence of this new intermediate wavelength mode may explain the complicated behavior observed in direct numerical simulations of the non-linear three-dimensional Navier-Stokes equations at low Reynolds numbers.