On the role of the laminar/turbulent interface in energy transfer between scales in bypass transition

Abstract

We investigate the role of the laminar/turbulent interface in the interscale energy transfer in a boundary layer undergoing bypass transition with the aid of the Kármán–Howarth–Monin–Hill (KHMH) equation. A local binary indicator function is used to detect the interface and employed subsequently to define two-point intermittencies. These are used to decompose the standard-averaged interscale and interspace energy fluxes into conditionally averaged components. We find that the inverse cascade in the streamwise direction reported in an earlier work arises due to events across the downstream or upstream interfaces of a turbulent spot. However, the three-dimensional energy flux maps reveal significant differences between these two regions: in the downstream interface, inverse cascade is stronger and dominant over a larger range of streamwise and spanwise separations. We explain this finding by considering a propagating spot of simplified shape as it crosses a fixed streamwise location. We derive also the conditionally averaged KHMH equation, thus generalising similar equations for single-point statistics to two-point statistics. We compare the three-dimensional maps of the conditionally averaged production and total energy flux within turbulent spots against the maps of standard-averaged quantities within the fully turbulent region. The results indicate remarkable dynamical similarities between turbulent spots and the fully turbulent region for two-point statistics. This has been known only for single-point quantities, and we demonstrate here that the similarity extends to two-point quantities as well.