Homotopy of exact coherent structures in plane shear flows

By Fabian Waleffe. 2003

309 citations recorded by the source corpus.

Subfields: Computational Mechanics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/d480421db094e1bf5a8898bbe7b513413151e283

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In Computational Mechanics

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Citations in the corpus

Visualizing the geometry of state space in plane Couette flow (2007, methodology): “As noted in Waleffe (2003), these solutions, and Clever & Busse (1992)’s equilibria of plane Couette flow with Rayleigh-Benard convection, are homotopic to the Nagata equilibria under smooth transformations in the flow conditions.”
Exact coherent structures in pipe flow: travelling wave solutions (2003, background): “1998), and travelling wave solutions in plane Poiseuille flow at Re = 977 (Waleffe 2003) compared to a transitional value of Re ≈ 2100 − 2300 (Rozhdestvensky & Simakin 1984, Keefe et al.”
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.”
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…”
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.”
On coherent structure in wall turbulence (2013, background): “These asymptotic nonlinear solutions have analogues at lower Reynolds numbers, for example, the vortex-wave interactions found numerically by Hall & Sherwin (2010), and the near-wall cycle (Waleffe 1997, 2003).”
The engine behind (wall) turbulence: perspectives on scale interactions (2017, background): “The relationships between invariant solutions and full turbulence have been explored by, e.g., Waleffe (2003) and Jiménez et al. (2005), and reviewed 817 P1-15 by Kawahara et al. (2012).”
The mechanism of streak formation in near-wall turbulence (2005, background): “However, Waleffe & Kim (1997) pointed out that this adjustment simply transforms the length-scale selection problem into the time-scale selection problem.”
Turbulence transition in pipe flow (2007, background): “For plane Poiseuille flow, these states appear as traveling waves from the beginning (Ehrenstein & Koch 1991, Waleffe 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).”
On the relevance of subcritical hydrodynamic turbulence to accretion disk transport (2005, background): “…in the recent years, in laboratory experiments (Daviaud et al. 1992; Dauchot & Daviaud 1995a,b; Bottin et al. 1997), numerical simulations (Hamilton et al. 1995; see also Schmiegel & Eckhardt 1997 and Eckhardt & Mersmann 1999), and theoretical analyzes (in particular Waleffe 1997; Waleffe 2003).”