A simplified model for flows with eddies in symmetrically expanding channels |
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Authors: | Shinya Watanabe Vakhtang Putkaradze |
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Affiliation: | 1. Department of Mathematical Sciences, Ibaraki University, Mito 310-8512, Japan;2. Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA |
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Abstract: | We derive a simplified model for two-dimensional (2D) channel flows with recirculated regions at moderate Reynolds numbers based on an extension of the boundary layer (BL) theory and averaging across the channel. The model reproduces symmetry-breaking bifurcations and resulting flow structures accurately. Analytical estimates for the decay rates toward the parabolic profile before and after a sudden change in the walls agree well with the full numerical simulations. A seemingly chaotic steady flow is also discovered in a channel with periodic expansions and contractions. |
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Keywords: | 47.20.Ky 47.15.Rq 47.15.Fe |
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