## 3 Results and Discussion
### Effect of Turbulence on Ignition Kernel Delay Time  
Figure 5 presents the effect of \(u^{\prime}\) on \(\tau_{\rm delay}\) for the early flame kernel development at \(d_{\rm gap}=2.0\) mm, in which there are five averaged data sets of \(\rm(d\)\(R\)/\(\rm d\)\(t\)) versus \(R\) at five different values of \(u^{\prime}\) varying from 0 to 2.1 m/s, similar to the five cases presented in Figure 3. Each datum is averaged from at least three repeated successful ignition runs using the same \(\rm E_{ig,L}\approx MIE_{L}\) for the laminar case and \(\rm E_{ig,T}\approx MIE_{T}\) at corresponding values of \(u^{\prime}\) for turbulent cases from Figure 2b are applied. As seen, \(\rm d\)\(R\)/\(\rm d\)\(t\) increases with increasing \(u^{\prime}\) that leads to a decrease of \(\tau_{\rm delay}\) as indicated in the inset of Figure 5a. These measured \(\rm(d\)\(R\)/\(\rm d\)\(t\))\({}_{\rm min}\) and \(\tau_{\rm delay}\) are then plotted in Figure 5b against \(u^{\prime}\). The result seems to indicate a transition of \(\tau_{\rm delay}\) that occurs at a critical \(u^{\prime}\)\({}_{\rm c}\approx 0.92\) m/s. When \(u^{\prime}<u^{\prime}\)\({}_{\rm c}\), \(\tau_{\rm delay}\) decreases slightly from 4.8 ms at \(u^{\prime}\) = 0 to 4.3 ms at \(u^{\prime}\approx 0.92\) m/s (only about 80% decrement). However, when \(u^{\prime}>u^{\prime}\)\({}_{\rm c}\), a more rapid decrease of \(\tau_{\rm delay}\) is found, where \(\tau_{\rm delay}\approx 4.3/3.7/2.8\) ms at \(u^{\prime}\) = 0.92/1.4/2.1 m/s, respectively. The decrease of \(\tau_{\rm delay}\) with increasing \(u^{\prime}\) is attributed to the flame kernel speed enhancement by turbulence, where corresponding values \(\rm(d\)\(R\)/\(\rm d\)\(t\))\({}_{\rm min}\) increase with \(u^{\prime}\). These results in Figure 5b reveal that turbulence in the pre-transition has a small influence on the early flame kernel development, as can be also seen from these sequential schlieren images in the 2 nd and 3 rd rows of Figure 3. In the post-transition at higher \(u^{\prime}>u^{\prime}\)\({}_{\rm c}\), turbulence can facilitate the growth rate of the early flame kernels (see the 4 th and 5 th rows in Figure 3), resulting in a more rapid reduction of \(\tau_{\rm delay}\). By comparing Figure 2b for the regular MIE transition with Figure 5b for the \(\tau_{\rm delay}\) transition, it is found  
Figure 4: (**a**) Flame speed of the early flame kernel development plotted against flame kernel radius at different \(\rm E_{ig}\) using the same experimental settings in quiescence, obtained from the raw flame kernel radii versus time (the inset figure). (**b**) The ignition kernel delay time (\(\tau_{\rm delay}\)) measured at \(R_{\rm Lmin}\approx 5.0\) mm, with the minimum flame speed \(\rm(d\)\(R\)/\(\rm d\)\(t\))\({}_{\rm min}\) plotted against the normalized \(\rm E_{ig}/MIE_{L}\).  
that both transitions are reversely dependent on each other. An increase of \(u^{\prime}\) accelerates the early flame kernel development with a shorter \(\tau_{\rm delay}\) that requires a sufficiently high MIET to overcome the turbulent convection heat losses; such a trend is even more profound when \(u^{\prime}>u^{\prime}_{\rm c}\) in the post-transition.