Attached eddy model revisited using a minimal quasi-linear approximation

The mean logarithm emerges with self-similar energy balance

“…2006; Hwang & Cossu 2011; Lozano-Durán & Jiménez 2014; Hwang 2015; McKeon 2017; Hwang & Sung 2018; Baars & Marusic 2020 a , b ) and supporting mathematical evidence from analysis of the Navier–Stokes equations (Hwang & Cossu 2010; Klewicki 2013; Moarref et al. 2013; Eckhardt & Zammert 2018; Doohan, Willis & Hwang 2019; Yang, Willis & Hwang 2019; Hwang & Eckhardt 2020).…”

Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

“…An eddy viscosity may be motivated by concepts underlying the triple decomposition (Reynolds & Tiederman 1967;Reynolds & Hussain 1972), which identifies the Reynolds stresses as acting on the coherent fluctuations (from both the coherent and incoherent fluctuations), even though the phase average used to define the coherent part of the turbulent viscosity field is ambiguous in unforced turbulent flows. Many studies have applied eddy-viscosity models in the wall-bounded turbulence literature (Del Alamo & Jimenez 2006;Pujals et al 2009;Hwang & Cossu 2010a,b;Hwang 2016;Vadarevu et al 2019;Hwang & Eckhardt 2020) either through implementation of the Cess (1958) model or by estimating the eddy-viscosity field via the Reynolds stresses and the mean shear rate of strain. Similarly, global stability analyses have applied eddy-viscosity models to identify and/or control forced or self-sustained resonances in transitional and turbulent flows (Crouch, Garbaruk & Magidov 2007;Meliga, Pujals & Serre 2012;Mettot, Sipp & Bézard 2014;Oberleithner, Paschereit & Wygnanski 2014;Sartor, Mettot & Sipp 2014;Rukes, Paschereit & Oberleithner 2016;Semeraro et al 2016a;Tammisola & Juniper 2016).…”

“…Finally, Pickering et al (2020b) used an eddy-viscosity enhanced resolvent model to reconstruct the large-eddy simulation (LES) acoustic field of transonic and supersonic turbulent jets at a significantly lower rank when compared to their non-eddy-viscosity enhanced computations. Other approaches have implemented eddy-viscosity fields to develop self-consistent models, such as Yim, Meliga & Gallaire (2019) or Hwang & Eckhardt (2020), where the former study coupled a harmonically forced, quasi-linear resolvent analysis with Reynolds-averaged Navier-Stokes (RANS) equations, citing eddy viscosity as a necessary link between the coherent and incoherent perturbation dynamics.…”

Spectral energetics of a quasilinear approximation in uniform shear turbulence

“…The modern approaches share similar ideas with these early ones, but they take more flexible and delicate approaches for modelling of the self-interaction term of the second group (e.g. stochastic forcing, eddy viscosity, etc); for example, stochastic structural stability theory (S3T) (Farrell & Ioannou 2007, 2012, direct statistical simulation (DSS) (Marston, Conover & Tobias 2008;Tobias & Marston 2013), self-consistent approximations (Mantič-Lugo, Arratia & Gallaire 2014; Mantič-Lugo & Gallaire 2016), restricted nonlinear model (RNL) (Thomas et al 2014(Thomas et al , 2015Farrell, Gayme & Ioannou 2017), generalised quasilinear approximations (GQL) (Marston, Chini & Tobias 2016;Tobias & Marston 2017) and minimal quasilinear approximation augmented with eddy viscosity (Hwang & Eckhardt 2020).…”

“…Or it can be combined with an ad-hoc model to deal with the ignored nonlinear energy transport (e.g. eddy viscosity model in Hwang & Eckhardt 2020) to keep the small degree of freedom of the QL models.…”