Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

Abstract

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Self-similar Rayleigh–Taylor mixing with accelerations varying in time and space

“…The departures from the Kolmogorov scaling laws appear to be clear in realistic turbulent processes ( 38 – 41 ). They are often referred to as “anomalous scaling.” Our analysis finds that RT/RM mixing with variable accelerations (in time and in space) belong to a special self-similar class and exhibit significant departures in terms of invariant, scaling, spectral, and correlation properties from Kolmogorov turbulence.…”

Extended proper orthogonal decomposition of non-homogeneous thermal fields in a turbulent pipe flow

“…Amongst the category of wall-bounded turbulent flows, pipe flows represent a canonical case which has been widely studied and is still object of intense research (see e.g. the recent thematic issue on high Reynolds number wall turbulence [1]). In spite of its importance and its wide range of applications in heat exchanger devices, literature is mostly focused on average heat transfer performance, starting from straight tubes (presented in well assessed textbooks, see, e.g.…”