No abstract

The role of the seam in the ‘swing’ of a cricket ball is investigated via unsteady force and surface-pressure measurements and oil-flow visualization in a low-turbulence wind tunnel. Various seam angles of the ball and flow speeds are considered. Static tests are carried out on a new ‘SG Test’ cricket ball as well as its idealized models: a smooth sphere with one and five trips. To study the effect of surface roughness of the ball as the game progresses, force measurements are also carried out on a cricket ball that is manually roughened, on one-half and completely, to model a ball that has been in play for approximately 40 overs (240 deliveries/balls). The Reynolds number ($Re$) is based on the free-stream speed and diameter of the respective model. A new cricket ball experiences three flow states with increase in $Re$: no swing (NS), conventional swing (CS) and reverse swing (RS). At relatively low $Re$, in the NS regime, the seam does not have any significant effect on the flow. The separation of the laminar boundary layer, with no subsequent reattachment, is almost axisymmetric with respect to the free-stream flow. Therefore, the ball does not experience any significant lateral force. Beyond a certain $Re$, the boundary layer on the seam side of the ball undergoes transition. The boundary layer on the non-seam side, however, continues to undergo a laminar separation with no reattachment, thereby creating a lateral force in the direction of the seam, leading to CS. The onset of the CS regime is marked by intermittent formation of a laminar separation bubble (LSB) on the surface of the ball in the region between the laminar separation of the boundary layer and its reattachment at a downstream location. Owing to the varying azimuthal location of the seam, with respect to the front stagnation point on the ball, the transition via LSB formation is localized to a specific region over the seam side. In other regions, the boundary layer either transitions directly without the formation of an LSB, or separates on encountering the seam with no further reattachment. The spatial extent of the region where the flow directly transitions to a turbulent state increases with increase in $Re$, while that of the LSB decreases. Interestingly, the flow dynamics is such that the magnitude of the swing force coefficient stays relatively constant with increase in $Re$. With further increase in $Re$, the boundary layer on the non-seam side undergoes a transition via formation of an LSB. This, along with an upstream shift of the separation point on the seam side, leads to a switch in the direction of the lateral force. It now acts away from the seam, and leads to RS. The transition from CS to RS occurs over a very narrow range of $Re$ wherein the flow intermittently switches between the two flow states. It is observed that the transition of the boundary layer on the seam side leads to an upstream shift of the separation point on the non-seam side at the onset of CS. A complementary effect is observed at the onset of RS. Experiments on a ball that is manually roughened bring out the relative effect of the seam and roughness on the transition of the boundary layer. Compared to a new ball, the magnitude of the maximum swing force coefficient for a rough ball is smaller during the CS regime, and larger during the RS regime. Unlike other models, the ball with roughened non-seam side and smooth seam side, for certain seam orientations, exhibits RS at relatively lower speeds and CS at higher speeds. The forces measured on the cricket ball are utilized to estimate the trajectory of the ball bowled at various initial speeds and seam angles. The lateral movement of the ball depends very significantly on the seam angle, surface roughness and speed of the ball at its delivery. The maximum lateral deviation of a new ball during RS is found to be less than half of that observed in CS. On the other hand, the lateral movement of a roughened ball during RS may significantly exceed its movement during CS. The range of the speed of the ball, for various seam orientations and surface roughnesses, are estimated wherein it undergoes CS, RS or one followed by the other. Optimal conditions are estimated for the desired lateral movement of the ball.

Abstract

The streamwise inclination angle of large wall-attached structures, in the log region of a canonical turbulent boundary layer, is estimated via spectral coherence analysis, and is found to be approximately $45^{\circ }$. This is consistent with assumptions used in prior attached eddy model-based simulations. Given that the inclination angle obtained via standard two-point correlations is influenced by the range of scales in the turbulent flow (Marusic, Phys. Fluids, vol. 13 (3), 2001, pp. 735–743), the present result is obtained by isolating the large wall-attached structures from the rest of the turbulence. This is achieved by introducing a spanwise offset between two hot-wire probes, synchronously measuring the streamwise velocity at a near-wall and log-region reference location, to assess the wall coherence. The methodology is shown to be effective by applying it to data sets across Reynolds numbers, $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3})$–$O(10^{6})$.

The phenomenon of drag crisis for uniform flow past a smooth sphere is investigated via experiments in a low-turbulence wind tunnel for $1.5\times 10^{5}\leqslant Re\leqslant 5.0\times 10^{5}$. The Reynolds number, $Re$, is based on the free-stream speed and the diameter of the sphere. Based on the activity related to the laminar separation bubble (LSB), the critical regime for the occurrence of drag crisis ($3.4\times 10^{5}<Re<4.4\times 10^{5}$) is further divided into three subregimes. The gradual decrease of mean drag coefficient ($\overline{C}_{D}$) with $Re$, in subregime I, is due to the increase of base pressure and suction near the shoulder of the sphere. The flow is devoid of an LSB in this regime. The coefficient $\overline{C}_{D}$ decreases very rapidly with increase in $Re$ in subregime II primarily due to the increase in mean base pressure ($\overline{C}_{P,b}$). This subregime is characterized by intermittent switching of $C_{D}$ and $C_{P,b}$ between bistable states. Statistical analysis of the surface-pressure and force coefficients relates this behaviour to the intermittent appearance/disappearance of the LSB. The two states of the flow are referred to as the LSB and non-LSB states. The frequency of appearance of the LSB and the duration of its stay increase with increase in $Re$. An intermittency factor $I_{f}$, defined as the fraction of time during which the LSB exists in the flow, is estimated at each $Re$. The value of $I_{f}$ is zero in subregime I and increases from zero to one, with increase in $Re$, in subregime II. The variation of $\overline{C}_{D}$ with $Re$ is found to follow the variation of ($1-I_{f}$) with $Re$. This shows that the decrease of $\overline{C}_{D}$ with increase in $Re$, during drag crisis, is primarily due to the increased probability of the LSB state as opposed to the non-LSB state. A spatio-temporal analysis of the surface pressure measured at various polar locations on the surface of the sphere confirms the axisymmetric nature of the intermittent LSB. In subregime III of the critical regime, the LSB exists at all time instants ($I_{f}=1$). The $\overline{C}_{D}$ value continues to decrease with $Re$ in this subregime due to increase in $\overline{C}_{P,b}$. Unlike the general belief that the decrease in $\overline{C}_{D}$ with increase in $Re$ is due only to the increase in $\overline{C}_{P,b}$, it is found that the increase in suction upstream of the shoulder of the sphere, with increase in $Re$, also plays an important role. In particular, in the high subcritical regime ($2.5\times 10^{5}<Re<3.4\times 10^{5}$), the gradual decrease in $\overline{C}_{D}$ with increase in $Re$ is due solely to the increase in suction in a region upstream of the shoulder of the sphere.

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The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics across almost a decade of flow Reynolds number (Reτ) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with Reτ. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with Reτ. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux.

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