Convectively unstable anti-symmetric waves in flows past bluff bodies

Abstract

The steady flow past a circular cylinder is investigated. Symmetry conditions are imposed along the centerline of the flow field. The variation of the structure of the recirculation zone with the Reynolds number is studied. The effect of the location of lateral boundary on the flow is analyzed and compared with results from earlier studies. The eddy length varies linearly with Re. Three kinds of solutions, based on eddy structure, are found for different location of the lateral boundary. Global linear stability analysis has been carried out in a translating frame to determine the convective modes for flow past a circular cylinder. It is found that, compared to the unrestricted flow, the symmetry conditions lead to a significant delay in the onset of convective instability. Detailed results are presented for the Re=500 flow when the lateral walls are located relatively far off (50 radius) from the cylinder. This situation is expected to be close to unbounded flow past a cylinder. The convectively unstable modes are found to be one of the three kinds. The ones traveling at very low streamwise speed are associated with large scale structures and relatively low frequency. The modes that travel with relatively larger speed lead to the instability of the shear layer and have higher temporal frequency and small scale spatial structure. Instabilities which travel at even higher speeds resemble a swirling flow structure. The results from the linear stability analysis are confirmed by carrying out direct time integration of the linearized disturbance equations. The disturbance field shows transient growth and grows by several orders of magnitude confirming that such flows act as amplifiers. The critical Re for the onset of convective instability is discussed in the context of earlier results from local analysis.