The Role Played by Swift Change of the Stability Characteristic of Mean Flow in Bypass Transition

Authors: Dong Ming, Su Caihong

Abstract:

The scenario of bypass transition is generally described as follows: the low-frequency disturbances in the free-stream may generate long stream-wise streaks in the boundary layer, which later may trigger secondary instability, leading to rapid increase of high-frequency disturbances. Then possibly turbulent spots emerge, and through their merging, lead to fully developed turbulence. This description, however, is insufficient in the sense that it does not provide the inherent mechanism of transition that during the transition, a large number of waves with different frequencies and wave numbers appear almost simultaneously, producing sufficiently large Reynolds stress, so the mean flow profile can change rapidly from laminar to turbulent. In this paper, such a mechanism will be figured out from analyzing DNS data of transition.

Keywords: boundary layer, breakdown, bypass transition, stability, streak.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327983

References:

[1] Klebanoff P S, Effect of freestream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc., 1971. Vol. 10, pp. 1323-1327.
[2] Ellingsen T, Palm E, Stability of linear flow. Physics of Fluids, 1975. Vol. 18, pp. 487-488
[3] Hultgren L, Gustavson L, Algebraic growth of disturbances in a laminar boundary layer. Physics of Fluids, 1981. Vol. 24, no. 6, pp. 1000-1004.
[4] Luchini P, Reynolds number independent instability of the boundary layer over a flat surface. J. Fluid Mech., 1996. Vol. 327, pp. 101-115.
[5] Andersson P, Berggren M, and Henningson D S, Optimal disturbances and bypass transition in boundary layers. Physics of Fluids, 1999. Vol. 11, no. 1, pp. 134-150
[6] Brandt L, Henningson D S, Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech., 2002. Vol. 472, pp. 229-261.
[7] Elofsson P A, Kawakami M, and Alfredsson P H, Experiments on the stability of streamwise streaks in plane Poiseuille flow. Physics of Fluids, 1999. Vol. 11, pp. 915-930
[8] Andersson P, et al., On the breakdown of boundary layer streaks. Journal of Fluid Mechanics, 2001. Vol. 428, pp. 29-60
[9] Asai M, Minagawa M, and Nishioka M, The instability and breakdown of a near-wall low-speed streak. J. Fluid Mech., 2002. Vol. 455, pp. 289-314
[10] Matsubara M, Alfredsson P H, Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech., 2001. Vol. 430, pp. 149-168
[11] Jacobs R G, Durbin P A, Simulations of bypass transition. J. Fluid Mech., 2001. Vol. 428, pp. 185-212
[12] Luo J, Wang X, and Zhou H, Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows. Science in China Ser. G Physics, Mechanics & Astronomy, 2005. Vol. 48, no. 2, pp. 228-236.
[13] Dong M, Zhang Y M, and Zhou H, A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers-PSE plus DNS. Applied Mathematics and Mechanics-English Edition, 2008. Vol. 29, no. 12, pp. 1527-1534.
[14] Ricco P, Luo J S, and Wu X, Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. J. Fluid Mech., 2011. Vol. 677, pp. 1-38.