The Significance of Simple Invariant Solutions in Turbulent Flows
By Genta Kawahara, Markus Uhlmann, Lennaert van Veen. 2011
334 citations recorded by the source corpus.
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple invariant sets, such as nonlinear equilibria and periodic solutions, in well-resolved Navier--Stokes flows. This review describes some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows. It is shown that the near-wall regeneration cycle of coherent structures can be reproduced by such solutions. The typical similarity laws of turbulence, i.e. the Prandtl wall law and the Kolmogorov law for the viscous range, as well as the pattern and intensity of turbulence-driven secondary flow in a square duct can also be represented by these simple invariant solutions.
Subfields: Computational Mechanics, Global and Planetary Change
View Paper: https://www.semanticscholar.org/paper/f50748cb36fd8027a0d7a1df8a06e798d6af10de
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- B. McKeon
- Javier Jiménez
- Dwight Barkley
- Rich R. Kerswell
- Gary J. Chandler
- Ivan Marusic
- Ati S. Sharma
- Nicholas Hutchins
In Global and Planetary Change
- B. McKeon
- Javier Jiménez
- Rich R. Kerswell
- Dwight Barkley
- Gary J. Chandler
- Ivan Marusic
- Robert D. Moser
- Nicholas Hutchins
Citations in the corpus
- The engine behind (wall) turbulence: perspectives on scale interactions (2017, background): “These are alternately called travelling wave solutions (TWSs; Gibson, Halcrow & Cvitanović 2008), exact coherent states (ECSs; Waleffe 2001) or, in the asymptotically high-Reynolds-number limit, vortex–wave interaction (VWI; Hall & Sherwin 2010).”
- Coherent structures in wall-bounded turbulence (2017, background): “A review can be found in Kawahara et al. (2012), but this is a rapidly growing field, and interested readers are”
- Theoretical perspective on the route to turbulence in a pipe (2016, background): “The significant advantage of this approach is that it makes direct connection to the self-sustaining process (Waleffe 1997) and to exact coherent structures underlying wall-bounded turbulence at moderate Reynolds numbers (Eckhardt et al. 2007; Kawahara et al. 2012).”
- Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow (2013, background): “…(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 reviews by Kerswell (2005), Eckhardt et al. (2007) and Kawahara et al. (2012)).”