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7 et al. [25], Noack et al. [26] for circular cylinder flows, Van Oudheusden [27] for square cylinder and Durgesh [28] for a flat plate model. The first two modes appear as phase-shifted versions of each other, which can be combined to produce the von Kármán vortices. Similarly modes 4 and 5 contribute to the higher harmonic of von Kármán vortices. Mode 3 appears to be a standing mode with no companion mode. In order to further understand these modes we look at the relation between the time varying coefficients. Figure 5 shows the phase averaged time varying coefficients for base case. It indicates that phase of the time varying coefficients of first and second modes are 90 degrees apart and the magnitude is of the same order, indicating that they represent the same coherent structure shifted in phase. Hence these two modes can be combined to produce the von Kármán vortices at any phase in the shedding process. Similarly modes four and five are also 90 degrees phase shifted pair. The wavelength of mode pair 4 and 5 corresponds to half wavelength of mode pair 1 and 2, and hence mode pair 4 and 5 shed at twice the frequency of mode pair 1 and 2. Therefore mode pair 4 and 5 forms the higher harmonic of mode pair 1 and 2 (which forms the von Kármán vortices). SPANWISE VORTICES Smoke flow visualization in the vertical (XY) plane at ReD = 2200 indicates formation of a von Kármán vortex street in the wake of the airfoil, as shown in Figure 6. Figure 6: Smoke visualization of the von Kármán vortices in the wake of the airfoil at ReD = 2200 The von Kármán vortex street can also be observed in the results (Figure 7) of numerical simulations at four free stream velocities of U 0.25m/s, 0.40m/s, 0.60m/s and 10m/s, which are equivalent to ReD = 500, 800, 1200, and 17,000 respectively. Figure 7 shows contours of vorticity magnitude on the mid-plane of the solution domain, for the four mentioned values of ReD. A decreasing trend in the thickness of the shear layer, as well as the length of the formation region, can be observed in Figure 7, as ReD is increased from 500 to 17,000. Figure 8 shows the phase averaged streakline plots showing the spanwise vortices at ReD = 2.4x104 obtained by the adding first two POD modes, obtained from the PIV measurments. In Table 1, the streamwise wavelength λx is determined directly by measuring the average distance of each two consecutive vortices shed from either corner of the trailing edge. The convective velocity UC is determined by dividing λx by the shedding period TS in case of the numerical simulations and experiments, and by measuring the displacement of vortices in a sequence of burst images in case of the flow visualization. The lowest value of Strouhal number (0.152), which is associated with the lowest ReD, is very close to the value of 0.158, reported by Ryan et al. in [10] for the same geometry and ReD. The highest value of Strouhal number (0.228), which is associated with the ReD = 17000, is also in 7

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9 STREAMWISE VORTICES Smoke flow visualization in the horizontal (XZ) plane at ReD = 2200, which is carried out by placing the airfoil parallel to the smoke wire, indicate that the von Kármán vortex street in the wake of the airfoil is accompanied by three dimensional instabilities. These three dimensional instabilities manifest as vertical vortices, which can be observed in Figure 9. The average spanwise spacing between pairs of counter-rotating vertical vortices in the snapshot shown (Figure 9) is found to be Z / D Figure 9: Smoke visualization of the secondary structures in the wake of the airfoil at ReD = 2200 (flow is from left to right) Results of the numerical simulations also indicate the presence of three dimensional structures in the wake, in the form of streamwise and vertical vorticity components. To analyze these three dimensional structures, the spatial and temporal variations of the streamwise and vertical vorticity are studied along spanwise lines at various downstream locations, which are shown in Figure 10. Figure 10 : Location of spanwise lines for probing spatial and temporal variations of vorticity in numerical simulations Figures 11 shows examples of spatial and temporal variations of the streamwise and vertical components of vorticity ( X and Y ). The figure shows variations at ReD = 17,000 along a spanwise line located at x/d=1.0 and y/d = 0.5. The similar pattern of emergence and evolution of streamwise and vertical vorticity components, which accompany the periodic shedding of spanwise vortices, can be observed clearly in this figure. The figure also indicates that the three dimensional instability of the spanwise vortices, which results in the pairs of counter-rotating streamwise and vertical vortices, occurs with a periodic nature across the span. It should be mentioned that although the vorticity structure is not exactly similar for all Reynolds numbers, a 9

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