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

TL;DR

This paper examines how the laminar/turbulent interface influences energy transfer across scales during bypass transition in boundary layers, revealing differences in inverse cascade strength at different interfaces and extending statistical analysis to two-point quantities.

Contribution

It introduces a method to analyze two-point energy flux statistics across the laminar/turbulent interface using the KHMH equation and binary interface detection, revealing new insights into energy transfer mechanisms.

Findings

Inverse cascade is stronger at downstream interfaces of turbulent spots.

Turbulent spots exhibit similar two-point statistical properties to fully turbulent regions.

The derived conditionally-averaged KHMH equation generalizes single-point to two-point statistics.

Abstract

We investigate the role of laminar/turbulent interface in the interscale energy transfer in a boundary layer undergoing bypass transition, with the aid of the Karman-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 (head or tail respectively) 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 show here that the similarity extends to two-point quantities as well.