Two-point correlations conditioned on the turbulent/nonturbulent interface in a turbulent temporal jet

This paper investigates one- and two-point correlations conditioned to the turbulent/nonturbulent interface (TNTI) of a planar turbulent temporal jet. A classical average, which is taken with respect to a spatially averaged TNTI location, is compared to two types of conditional averages, which are conditioned with respect to the instantaneous TNTI. We show that the two conditional averages differ from the classical average, especially in the TNTI region and over a distance that is comparable to the standard deviation of the instantaneous TNTI location. All correlations scale in a self-similar manner with time when normalized with a characteristic jet width calculated from integral quantities of momentum and volume fluxes. This paper presents a two-dimensional framework of separation between the correlation points and physical position from the TNTI to show interesting behavior related to the location, size, and intensity of velocity fluctuations with respect to the TNTI. We observe that the conditional velocity correlation functions exhibit distinct peaks at well-defined separations, indicating the typical scales of turbulent motions influenced by the TNTI. The values of the relevant peaks clearly demonstrate that, even when studied in a conditional framework, the dynamics of the velocity fluctuations with respect to, for example, the enstrophy, shows the presence of length scales that are very large with respect to the width of the turbulent region. Interesting results emerge when the correlation where one point is always fixed on the TNTI and the other interrogates the turbulent zone is considered. This observable investigates the turbulent dynamics inside the turbulent zone with respect to the TNTI. We show that the peak correlations are in line with the standard deviation of the TNTI, suggesting a connection to the scale of the turbulent motions attached to the TNTI. These features are not captured in classical statistics or in prior TNTI studies relying solely on one-point quantities.