Confluence of flow past an array of circular cylinders and its transition to turbulence.

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Interactions of wakes in a flow past a row of square or circular bars are investigated theoretically, numerically and experimentally. At small Reynolds numbers the flow is steady and symmetric with respect not only to stream-wise lines through the center of each bar but also to stream-wise centerlines between adjacent bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and makes a transition to a steady asymmetric flow with respect to the centerlines between adjacent bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the … More transitions are evaluated numerically and the bifurcation diagram of the flow is obtained. These new findings were published in an article in Fluid Dynamics Research in 2002. In 2003 and 2004, the instability and transition of flow past two circular cylinders arranged in tandem are investigated numerically. We obtained the symmetric flow numerically and analyzed its stability by applying the linear stability theory. The nonlinear oscillatory flow arising from the instability was obtained not only by numerical simulation but also by direct numerical calculation of the equilibrium solution, and the bifurcation diagram for the nonlinear equilibrium solution is depicted. The transition of the flow from a steady state to an oscillatory state is clarified to occur due to a supercritical or sub-critical Hopf bifurcation depending upon the gap spacing. We found that there is a certain range of the gap spacing where physical quantities such as the drag and lift coefficients and the Strouhal number show an abrupt change when the gap spacing is continuously changed. We identified the origin of the abrupt change as the existence of multiple stable solutions for the flow. The paper including these results is published in the Physics of Fluids in 2005. Less