Towards a model of large scale dynamics in transitional wall-bounded flows

TL;DR

This paper introduces a simplified model for large-scale flow dynamics in transitional wall-bounded flows, capturing feedback interactions and turbulence self-sustainment mechanisms.

Contribution

It presents a novel set of equations that integrate large-scale flow interactions with turbulence modeling based on an extension of Waleffe's approach.

Findings

The model effectively captures large-scale flow behaviors in transitional regimes.

It links small-scale turbulence generation to large-scale flow dynamics.

Provides a framework for further analysis of laminar-turbulent transition processes.

Abstract

A system of simplified equations is proposed to govern the feedback interactions of large-scale flows present in laminar-turbulent patterns of transitional wall-bounded flows, with small-scale Reynolds stresses generated by the self-sustainment process of turbulence itself modeled using an extension of Waleffe's approach (Phys. Fluids 9 (1997) 883-900), the detailed expression of which is displayed as an annex to the main text.