POSTER: On bifurcations and traction forces on an obstacle in incompressible flow

Abstract

We present a systematic numerical investigation of bifurcations in the two-dimensional incompressible Navier--Stokes flow past a confined circular cylinder. In particular, we analyse the relation between traction profiles and qualitative changes in its long-time flow behavior. The results indicate a clear correspondence between changes in the traction profiles of the steady Navier--Stokes equations and bifurcations of the unsteady Navier--Stokes equations, including the manifestation of symmetry breaking, oscillations, and multiple steady solutions. While long-time flow behavior is often explored through direct numerical simulation of the unsteady equations, which is accurate but computationally demanding, these results suggest a more inexpensive strategy to detect critical Reynolds numbers.