# Investigation of Reverse Swing and Magnus Effect on a Cricket Ball Using Particle Image Velocimetry
## 4 Swing and the Separation Bubble  
For the initial set of experiments, the ball was not subject to rotation (\(\alpha=0\)) and CS was first studied. Figure 8 shows the time-averaged velocity magnitude as a fraction of the freestream (\(V/\!\!/\!I_{\infty}\)) and streamlines around the ball at a flow condition of \(\mathrm{Re}=1.1\times 10^{5}\) (equivalent to a bowling speed of 54 mph). The image is formed by superposing two sets of data from separate investigations of the SS and NSS. The flow field clearly shows conventional swing. On the NSS, where the flow stagnates, the smoother surface encourages a laminar boundary layer; flow separation occurs in an adverse pressure gradient at an angle \(\theta_{\mathrm{L}}\)\(\sim\)95\({}^{\circ}\). On the other hemisphere, the seam trips the boundary layer to turbulence and separation is delayed to \(\theta_{\mathrm{T}}\)\(\sim\)120\({}^{\circ}\). Note that the separation angle on the NSS is slightly higher than the data for the hydraulically smooth sphere shown in Figure 2; as discussed above, the rapid prototype surface finish is rougher than that of a manufactured new ball (equivalent to approximately 25 overs old or \(k/\!\!/d=250\times 10^{-5}\)). Figure 8: Time-averaged velocity magnitude and streamlines at \(U_{\infty}=12\) m/s, \(\mathrm{Re}=1.1\times 10^{5}\) (equivalent bowling speed of 54 mph), showing conventional swing, on the seam side \(\theta_{\mathrm{T}}\)\(\sim\)120\({}^{\circ}\) and on the non-seam side \(\theta_{\mathrm{L}}\)\(\sim\)95\({}^{\circ}\). Separation angles shown to nearest 5\({}^{\circ}\). Figure 7: Position of the ball to investigate (**a**) the non-seam side (NSS) and (**b**) the seam side (SS). Figure 9 shows a magnified view of the flow field at higher Re, revealing the region of separation on the NSS of a stationary ball. The data is collected over a range of Re specifically near, within, and either side of the critical regime--see Figure 3. At Re = \(1.35\times 10^{5}\) (Figure 9a), laminar separation still occurs at an angle of \(\theta_{\rm L}\)\(\sim\)100\({}^{\circ}\). As Re increases to \(1.65\times 10^{5}\) (Figure 9b-d), there is evidence that a separation bubble forms near the surface, shown by a localized region of recirculation. In addition, the separation point translates downstream. At higher Reynolds numbers (Re = \(1.69\times 10^{5}\) and \(1.74\times 10^{5}\) in Figure 9e,f), the laminar separation bubble reattaches downstream, and a turbulent separation angle can be identified around \(\theta_{\rm T}\)\(\sim\)130\({}^{\circ}\). The Reynolds number at which the separation bubble forms (and the flow enters the critical regime) is similar to that measured by [PERSON] et al. (2013), identified at the point where the direction of swing switched from CS to RS (see Figure 3). The range of Reynolds numbers shown here corroborates with the critical regime for a sphere with a surface roughness of \(k/d=250\times 10^{-5}\). The laminar separation bubble can be highly unsteady around the critical Reynolds number, as demonstrated by [PERSON] et al. (2015). Figure 10 shows two velocity \"snapshots\" at the same Re. Figure 10a clearly shows the formation of the bubble, and a corresponding smaller wake, whereas Figure 10b shows that the flow has separated earlier, with a corresponding larger wake. This illustrates the unsteadiness of the LSB, when operating close to the interface of the subcritical and critical flow regimes. Figure 9: Time-averaged velocity magnitude and streamlines with varying Re at a magnified region on the non-seam side, showing the formation of the separation bubble at \(\alpha\) = 0 (equivalent bowling speeds between 62 and 81 mph). Separation and reattachment angles shown to nearest 5\({}^{\circ}\). As discussed above, the swinging ball will feature backspin in a cricket match. The separation bubble is potentially destabilized by the rotation, which may exaggerate the surface roughness and any other protrusions or irregularities (i.e., the quarter seam and logo embossment).