Self-similar hierarchies and attached eddies

Attached eddy model revisited using a minimal quasi-linear approximation

“…A growing body of recent theoretical, numerical and experimental evidence has consistently supported the notion that wall-bounded turbulent shear flows, such as channel, pipe and boundary-layer flows, at high Reynolds numbers are composed of self-similar energy-containing motions throughout the logarithmic region (see a recent review by Marusic & Monty (2019)). For example, statistical evidence supporting the theoretical predictions of the original attached eddy model and its extensions (Marusic & Kunkel 2003;Tomkins & Adrian 2003;Jiménez & Hoyas 2008;Marusic et al 2013;Baars & Marusic 2020a,b), direct confirmations on the existence of self-similar energy-containing motions Hwang & Cossu 2010c, 2011Lozano-Durán & Jiménez 2014;Hwang 2015;Hellstöm, Marusic & Smits 2016;Hwang & Bengana 2016;Hwang & Sung 2018) and supporting mathematical evidence from analysis of the linearised and full Navier-Stokes equations Hwang & Cossu 2010b;Klewicki 2013;Moarref et al 2013;Hwang, Willis & Cossu 2016;Eckhardt & Zammert 2018;Doohan, Willis & Hwang 2019;McKeon 2019;Vadarevu et al 2019;Yang, Willis & Hwang 2019).…”

Uniform-momentum zones in a turbulent boundary layer subjected to freestream turbulence

“…2016), where is the friction velocity, is the boundary layer thickness and is the kinematic viscosity. These instantaneous flow features were also observed through reduced-order models of the large-scale coherence in TBLs based on the Navier–Stokes equations (Saxton-Fox & McKeon 2017; McKeon 2019). Furthermore, UMZs have been used in models that are able to reproduce boundary layer statistics up to fourth order (Bautista et al.…”

Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows

“…The fact that the log-layer structure of the minimal flow unit spans the full boundary layer thickness can be further explained by the self-similar attached-eddy hypothesis (Townsend 1976; Perry & Chong 1982; Meneveau & Marusic 2013; Agostini & Leschziner 2017; Marusic & Monty 2019). McKeon (2019) has recently identified that an isolated resolvent mode with a given convection velocity constitutes only part of the full attached eddy, and a geometric progression of such modes needs to be considered for the fair comparison to the attached eddies. In particular, a single wall-normal location of the log layer will be affected by a series of wall-attached eddies whose footprint includes the given wall-normal height.…”