On the evolution of the velocity gradient tensor in transitional boundary layers

TL;DR

This paper investigates the evolution of the velocity gradient tensor during the transition from laminar to turbulent boundary layers, using derived transport equations and invariant analysis to understand nonlinear structure development.

Contribution

It introduces a novel approach using invariant-based transport equations to analyze the velocity gradient tensor during transition, aiding future turbulence modeling.

Findings

Identification of key invariants during transition

Development of integral budgets for different transition stages

Discussion on suitable quantities for modeling applications

Abstract

We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the Q-criterion. To that end, we have derived transport equations based on several invariants of the velocity gradient tensor to obtain integral budgets spanning the different stages of transition from laminar to turbulent flow. We have also discussed which quantity would be the most appropriate in our study, while keeping in mind the potential for future modeling applications.