Stability Characteristics of Linear Unstable Modes in Flow Past Elliptic Cylinders

Linear stability analysis of steady two-dimensional flow past elliptic cylinders with different aspect ratios (Ar) has been conducted for Reynolds number (Re) up to 200. The main characteristics of the steady flow (bubble length, bubble width, drag coefficient, and maximum vorticity on the cylinder surface) have been presented. From the linear stability computations, we find that there are three sets of complex eigenmodes which become unstable with increasing Re. We refer to them as primary wake mode (PWM), secondary wake mode, and tertiary wake mode (TWM), respectively. PWM and SWM have already been reported in the literature for flow past a circular cylinder. In this work, we report a new unstable mode (TWM) along with PWM and SWM in the wake of elliptic cylinders. The structure of TWM shows that it is not so prominent in the near wake but has the longest range of presence and extends all the way up to the downstream boundary. The critical Re for the onset of instability of these modes and the corresponding Strouhal number (St) have been computed. Least-square fit equations for critical Re and St as a function of Ar have also been presented.