Abstract
It is traditionally understood that laminar-turbulent transitions of wall shear flows are induced through two steps of instability, linear and nonlinear ones. The linear instability occurs at an early stage of the transition process and amplifies proper unstable waves selected from small disturbances existing in the flow. This instability has been investigated by many researchers with the Orr-Sommerfeld equation in the linear stability equations[1]. As a result, it has been found in plane Poiseuille flow that unstable Tollmien-Schlichting (hereafter, TS in short) waves are amplified exponentially with proper growth rates calculated as the eigenvalues of the Orr-Sommerfeld equation. Furthermore, the critical Reynolds number for the TS wave is derived as 5772[2]. On the other hand, the nonlinear instability is induced by the linearly amplified TS waves and amplifies various three-dimensional disturbances existing in the flow. Thus, this instability occurs usually at the final stage of the transition process and completes the transition process to turbulence.
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© 2001 Springer Science+Business Media Dordrecht
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Yamamoto, K., Takahashi, N., Kambe, T. (2001). Direct Numerical Simulation of Transition in Plane Poiseuille Flow. In: Kambe, T., Nakano, T., Miyauchi, T. (eds) IUTAM Symposium on Geometry and Statistics of Turbulence. Fluid Mechanics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9638-1_38
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DOI: https://doi.org/10.1007/978-94-015-9638-1_38
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