Self-Sustaining Process of Townsend’s Attached Eddies in High-Reynolds-Number Wall Turbulence

Over the past decade, significant progress on understanding the coherent structures in wall turbulence has been made, especially in twofold. One is discovery of the non-trivial exact solutions of the Navier-Stokes equation, known as exact coherent structures, which has allowed for tackling low-Reynolds-number turbulence with dynamical system approaches. The other, initiated by discovery of new coherent structures emerging much further from wall at high Reynolds numbers, is the emerging evidence supporting Townsend's attached eddy hypothesis, which views that all the coherent structures, the size of which varies from the inner to outer length scale, are self-similar and form a hierarchial organisation.

Recently, the single eddy entity in the hierarchial organisation, called attached eddy, has been computed by our group, providing compelling evidence on the existence of the attached eddy. It has been found that the computed attached eddies exhibit the physical features highly reminiscent of those of the exact coherent structures. The goal of the proposed research is therefore to establish a theoretical link between the Townsend's attached eddies and the exact coherent structures in high-Reynolds-number wall turbulence. To achieve this, two work packages are proposed, one of which is to examine the detailed physical processes of a single attached eddy (especially streak instability) and the other is to directly compute the exact coherent structures associated with the given attached eddy.

The proposed research will be an important step towards a consistent theoretical description of statistical and dynamical features of the coherent structures in a wide range of the Reynolds numbers, covering from transitional (especially bypass transition) to fully-developed turbulent regime. It will also have a great potential to contribute to understanding and controlling wall turbulence at high Reynolds numbers, crucial for development of next generation aeronautical and mechanical engineering devices.

The proposed research is concerned with the understanding of the fundamental physical processes of coherent structures in wall turbulence by establishing a link between two state-of-the-art theoretical ideas, Townsend's attached eddy hypothesis and exact coherent structures. Given the recent finding that the attached eddies (i.e. the coherent structures at all the length scales varying from the inner to outer units at high Reynolds numbers) are involved in a significant amount of turbulent skin-friction drag, the outcome of the proposed research will subsequently play an important role in illuminating the mechanism of turbulent skin-friction generation at high Reynolds numbers. The precise understanding of turbulent skin-friction generation mechanism is very important especially for design of novel wall-based control strategies for turbulent drag reduction, which can create direct impact on numerous engineering applications, such as design of aircraft wings, ship hulls and turbine blades, construction of pipelines for transport of gas and oil, onshore wind-energy farming, sediment and pollution transport, and many others.

The proposed research will therefore potentially contribute to the manufacturing sector, a crucial part of the UK economy. In particular, it will create a basic knowledge required for aeronautical and mechanical industries, contributing to the sector's international competitiveness. The proposed research will also train postgraduate and undergraduate students, and will be acting as a pipeline for producing internationally competent aeronautical engineers. A public engagement is finally proposed for a societal contribution through Imperial Science Festival and HEADSTART Summer School.