On coherent structure in wall turbulence

TL;DR

This paper introduces a new theory predicting coherent structures like hairpin vortices in wall turbulence, based on Navier-Stokes analysis and low-dimensional flow dynamics, supported by comparisons to experimental and simulation data.

Contribution

It is the first to predict turbulence structures such as hairpin vortices from fundamental Navier-Stokes equations using a critical layer mechanism.

Findings

Predicts hairpin vortices and packets from response modes

Explains large-scale motions organizing hairpins

Links coherence to classical Kelvin-Stuart vortices

Abstract

A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier-Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech, 658, 2010), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially-varying travelling waves. By way of example, simple combinations of these modes are offered that predicts hairpins and modulated hairpin packets. The phase interaction also predicts important skewness and correlation results known in the literature. It is also shown that the very large scale motions act to organise hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally varying the shear profile. The relationship between Taylor's hypothesis and coherence is discussed and both are shown to be the consequence of the localisation of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin-Stuart (cat's eye) vortices. Evidence for the theory is presented based on comparison to observations of structure reported in the experimental, transitional flow and turbulent flow numerical simulation literature.