Abstract
The prevailing mathematical model describing the laminar–turbulent transition in a circular pipe is based on a full system of Navier–Stokes equations. Calculations using this model are very expensive; in addition, the computed dynamics is chaotic and too complex to decode the transition scenario. In the present study we consider certain simplifications, including popular cases restricting the dynamics to reflectional and rotational symmetries. We show that in these two cases transitional and turbulent flows cannot be computed properly.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1028335821100037/MediaObjects/11446_2022_1336_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1028335821100037/MediaObjects/11446_2022_1336_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1028335821100037/MediaObjects/11446_2022_1336_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS1028335821100037/MediaObjects/11446_2022_1336_Fig4_HTML.png)
Similar content being viewed by others
REFERENCES
V. G. Priymak and T. Miyazaki, J. Comput. Phys. 142, 370 (1998).
V. G. Priymak, Phys. Fluids 30, 064102 (2018).
D. Barkley, J. Fluid Mech. 803, 1 (2016).
V. C. Patel and M. R. Head, J. Fluid Mech. 38, 181 (1969).
D. Samanta, A. de Lozar, and B. Hof, J. Fluid Mech. 681, 193 (2011).
L. Shemer, I. Wygnanski, and E. Kit, J. Fluid Mech. 153, 313 (1985).
P. Ritter, F. Mellibovsky, and M. Avila, New J. Phys. 18, 083031 (2016).
N. V. Nikitin and V. O. Pimanov, Fluid Dyn. 53, 65 (2018).
N. B. Budanur, A. S. Dogra, and B. Hof, Phys. Rev. Fluids 4, 102401 (2019).
ACKNOWLEDGMENTS
The author is grateful to O.G. Chkhetiani for helpful discussions of this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Priymak, V.G. Navier–Stokes Solutions with Symmetry Constraints and Their Relation with Transitional and Turbulent Pipe Flows. Dokl. Phys. 66, 293–295 (2021). https://doi.org/10.1134/S1028335821100037
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335821100037