STREAMWISE DISTANCE, x/x LT

line that fits the data in the early stage of transition always has a smaller slope than the one that fits the data in the latter stage and indicates that the spot production rate is smaller in the earlier stage than in the latter. In addition, the intercept x, determined by the line in the latter stage is always about midway through the first stage and indicates that the produc-tion of turbulent spots as determined from the data in the latter stage is a result of something happening midway through the first. Narasimha et al. refer to this early stage of transition as "sub-transition. " Here, however, it is proposed that the "first stage " of transition in favorable pressure gradients is simply an extended region over which turbulent spots are produced. That is, for favorable pressure gradients, Eq. (4) in the text is not a good approximation for the spot production function g(Po) and should be replaced by a function that reflects a production of spots over an extended region. lfg(P0) is replaced by a Gaussian distribution, which has a standard deviation equal to two percent of the transition length, the curves shown in Figs. B3 and B4 result. In Fig. B3 the normalized Gaussian production function and resulting intermittency distribution are shown. In Fig. B4, a curve that can be approximated by two straight lines is quite evident. Therefore, it is suggested that turbulent spots are really produced over an extended re-gion in the flow, unlike Dhawan and Narasimha's (1958) con-clusion, and that this region is significant for transition in flows with a favorable pressure gradient. For transition in flows with an adverse pressure gradient, turbulent spots appear to be produced within a region that is narrow compared to the length of transition. All the results shown in the text for fa-vorable pressure gradients were reduced using the data in the latter stage of transition