Exact coherent structures in pipe flow: travelling wave solutions

By H. Wedin, Rich R. Kerswell. Journal of Fluid Mechanics, 2003

417 citations recorded by the source corpus.

Subfields: Computational Mechanics, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/b638c88f1ac80ed99c9a7f3476d1169a9283d2d8

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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, background): “The invariant manifolds tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of continuous and discrete symmetry-induced heteroclinic connections.”
An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows (2007, background): “Very recently, both this qualitative scenario and these quantitative predictions have been confirmed explicitly by experiments [5] and numerical studies [64–66], see Figs.”
On coherent structure in wall turbulence (2013, background): “In a pipe, solutions have been found by Wedin & Kerswell (2004), Kerswell (2005), Duguet, Willis & Kerswell (2008, 2010) and Pringle, Duguet & Kerswell (2009); these have tended to take the form of self-interacting rolls and streaks.”
Large-scale and very-large-scale motions in turbulent pipe flow (2006, background): “The interesting recent results on large-scale motions in transitional flow (Hof et al. 2004), and long, exact travelling wave solutions for low-Reynolds-number pipe flow (Wedin & Kerswell 2004; Priymak & Miyazaki 2004; Waleffe & Wang 2005) are intriguing in this regard.”
Theoretical perspective on the route to turbulence in a pipe (2016, background): “(See Waleffe (1997), Faisst & Eckhardt (2003), Wedin & Kerswell (2004), Eckhardt et al. (2007), Kawahara, Uhlmann & van Veen (2012) for details of the coherent structures of wall-bounded turbulence, structures that will be here treated as microscopic.”
A critical-layer framework for turbulent pipe flow (2010, background): “Subsequently, there has been much interest in the importance and observability of travelling wave solutions of the Navier–Stokes equations, e.g. Wedin & Kerswell (2004) and Viswanath (2009) in pipe flow (which, of course, is also linearly stable).”
Transition in pipe flow: the saddle structure on the boundary of turbulence (2007, methodology): “These new waves are significant because they appear much earlier in Re than the originally discovered TWs (Faisst & Eckhardt 2003; Wedin & Kerswell 2004) and their upper-branch solutions look more highly nonlinear.”
Turbulence transition in pipe flow (2007, background): “The detailed choice of body force is not critical: Wedin & Kerswell (2004) first solved the linear system and used the least-damped streamwise rolls as a starting point, but the intuitive choice of Faisst & Eckhardt (2003) leads to the same coherent states.”
Instability of Taylor-Couette flow between concentric rotating cylinders (2005, neutral): “For the pipe flow, in a recent study, Wedin and Kerswell [31] showed the presence of a "shoulder" in the velocity profile at about r/R=0.6 from their traveling wave solution.”
Measurement of laminar, transitional and turbulent pipe flow using Stereoscopic-PIV (2007, background): “…(Trefethen et al. 1993; Schmid and Henningson et al. 1994), the establishment of a self-sustained non-linear process (Waleffe 1997), and the organization of the flow around a few dominant exact solutions of the Navier–Stokes equations (Faisst and Eckhardt 2003; Wedin and Kerswell 2004).”