With decreasing Reynolds number, Re, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of Re lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.
Journal of Fluid Mechanics
The authors thank S. Zammert and B. Budanur for useful discussions. J. F. Gibson is gratefully acknowledged for the development and the maintenance of the code Channelflow. Y.D. would like to thank P. Schlatter and D. S. Henningson for an early collaboration on a similar topic in the case of plane Couette flow during the years 2008–2013.
Paranjape CS, Duguet Y, Hof B. Oblique stripe solutions of channel flow. Journal of Fluid Mechanics. 2020;897. doi:10.1017/jfm.2020.322
Paranjape, C. S., Duguet, Y., & Hof, B. (2020). Oblique stripe solutions of channel flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2020.322
Paranjape, Chaitanya S, Yohann Duguet, and Björn Hof. “Oblique Stripe Solutions of Channel Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2020. https://doi.org/10.1017/jfm.2020.322.
C. S. Paranjape, Y. Duguet, and B. Hof, “Oblique stripe solutions of channel flow,” Journal of Fluid Mechanics, vol. 897. Cambridge University Press, 2020.
Paranjape CS, Duguet Y, Hof B. 2020. Oblique stripe solutions of channel flow. Journal of Fluid Mechanics. 897, A7.
Paranjape, Chaitanya S., et al. “Oblique Stripe Solutions of Channel Flow.” Journal of Fluid Mechanics, vol. 897, A7, Cambridge University Press, 2020, doi:10.1017/jfm.2020.322.
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