Exact coherent structures in channel flow

By Fabian Waleffe. Journal of Fluid Mechanics, 2001

323 citations recorded by the source corpus.

Subfields: Computational Mechanics, Global and Planetary Change, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/ec87f67d4c9c26467820cdb3b10b947d56f002f5

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Citations in the corpus

Interaction between a large-scale structure and near-wall structures in channel flow (2005, background): “…has been established by direct numerical simulation (DNS) of filtered flows (Jiménez & Simens 2001), the discovery of travelling-wave solutions (Waleffe 1998, 2001, 2003; Itano & Toh 2001) and time-periodic solutions (Kawahara & Kida 2001; Toh & Itano 2003) of the Navier–Stokes equations.”
Turbulence transition in pipe flow (2007, background): “They have the additional bonus of being exact solutions to the equations of motion, which is why the term “exact coherent structures” has been suggested (Waleffe 1998, 2001, 2003).”
Statistical structure of self-sustaining attached eddies in turbulent channel flow (2015, background): “…the exact solutions of the Navier–Stokes equation given in the form of unstable equilibria, travelling waves, and periodic orbits (e.g. Nagata 1990; Waleffe 1998, 2001, 2003; Faisst & Eckhardt 2003; Wedin & Kerswell 2004; Jiménez et al. 2005; Gibson, Halcrow & Cvitanovic 2008; Hall & Sherwin…”
Coherent structures in wall-bounded turbulence (2017, background): “These solutions have often been described as “exact coherent structures” (Waleffe 2001), which they strongly resemble (Jiménez et al.”
The large-scale dynamics of near-wall turbulence (2002, methodology): “Fully nonlinear individual structures of similar sizes have been isolated by different methods in simplified Poiseuille (Jiménez & Moin 1991; Jiménez & Simens 2001; Waleffe 2001) and Couette flows (Nagata 1990; Waleffe 1998; Kawahara & Kida 2001).”
A critical-layer framework for turbulent pipe flow (2010, methodology): “Waleffe (1997, 2001, 2003) followed a different approach, developing exact solutions of the Navier–Stokes equations that give rise to unstable coherent structures which they propose form the foundations of transitional flow and nearwall turbulence.”
Visualizing the geometry of state space in plane Couette flow (2007, methodology): “Starting with physical insights from the self-sustaining process theory, Waleffe (1998, 2001, 2003) generated, ab initio, families of exact 3D equilibria and traveling waves of Navier-Stokes in plane Couette and Poiseuille flows for a variety of boundary conditions and Re numbers, using a 104-dime”
Interactions within the turbulent boundary layer at high Reynolds number (2011, background): “While the latter structures have been well documented and some theoretical and conceptual arguments have been provided to link near-wall streaks with hairpin-like vortices and hairpin packets (Adrian, Meinhart & Tomkins 2000; Waleffe 2001; Adrian 2007), the formation, evolution and characteristics o”
Recurrent motions within plane Couette turbulence (2006, background): “Although approximate, some mechanisms can be useful for computing exact solutions, as shown by the construction of travelling-wave and steady solutions of channel flows by Waleffe (1998, 2001, 2003).”
Transition in pipe flow: the saddle structure on the boundary of turbulence (2007, background): “These exact solutions are travelling waves (TWs) which appear through saddle-node bifurcations as in other shear flows (Nagata 1990; Waleffe 1997, 1998, 2001, 2003).”
Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow (2013, background): “…this quasi-cycle turned out to indicate the presence of families of exact (unstable) travelling wave (TW) solutions to the Navier–Stokes equations (Waleffe 1998, 2001, 2003), the existence of which have revolutionized our thinking about transitional and weakly turbulent shear flows (see the…”
The engine behind (wall) turbulence: perspectives on scale interactions (2017, background): “Waleffe (2001) subsequently formalized the description of the dynamics of the underlying SSP. Exact coherent states have been found in all of the canonical flows, in chronological order of discovery: plane Couette, channel, pipe and boundary layer flows.”
The Significance of Simple Invariant Solutions in Turbulent Flows (2011, methodology): “In order to relate a nonlinear equilibrium state with the self-sustaining process of buffer-layer coherent structures Waleffe (2001, 2003) introduced a spanwise periodic array of streamwise-independent rolls as external forcing to the Navier– Stokes equation.”