Abstract
Three nonlinear travelling wave solutions for square duct flow are discovered. One of them, the asymmetric solution, which is predicted by the stability analysis, bifurcates from the mirror-symmetric solution found by Okino et al., J. Fluid Mech. 657, 413 (2010). The solution is characterized by asymmetric crosssectional flow patterns with streamwise vortices attached to one of the side walls. The other two solutions, which have rotational symmetry by π and π /2, respectively, are found by a homotopy approach using artificially arranged body forces. Each of the new solutions shows striking similarity to that of pipe flow.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biau, D., Bottaro, A.: Phil. Trans. Roy. Soc. A 367, 529 (2009)
Faisst, H., Eckhardt, B.: Phys. Rev. Lett. 91, 224502 (2003)
Okino, S., Nagata, M., Wedin, H., Bottaro, A.: J. Fluid Mech. 657, 413 (2009)
Pringle, C.C.T., Kerswell, R.R.: Phys. Rev. Lett. 99, 074502 (2007)
Pringle, C.C.T., Duguet, Y., Kerswell, R.R.: Phil. Trans. Roy. Soc. A 367, 457 (2009)
Uhlmann, M., Nagata, M.: J. Fluid Mech. 551, 387 (2006)
Uhlmann, M., Pinelli, A., Kawahara, G., Sekimoto, A.: J. Fluid Mech. 588, 153 (2007)
Uhlmann, M., Kawahara, G., Pinelli, A.: Phys. Fluids 22, 084102 (2010)
Waleffe, F.: Phys. Rev. Lett. 81, 4140 (1998)
Wedin, H., Kerswell, R.R.: J. Fluid Mech. 508, 333 (2004)
Wedin, H., Bottaro, A., Nagata, M.: Phys. Rev. E 79, 065305 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Okino, S., Nagata, M., Wedin, H., Bottaro, A. (2012). Travelling Wave Solutions in Square Duct Flow. In: Oberlack, M., Peinke, J., Talamelli, A., Castillo, L., Hölling, M. (eds) Progress in Turbulence and Wind Energy IV. Springer Proceedings in Physics, vol 141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28968-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-28968-2_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28967-5
Online ISBN: 978-3-642-28968-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)