Abstract
The transition to turbulence in a square duct is an intriguing problem of hydrodynamics and has been studied since the work by Nikuradse [5]. The mean secondary flow of the turbulent state is made up by 8 vortices in the cross-sectional plane with 2 vortices in each corner, symmetric about the diagonals [2, 3, 5, 6, 7, 8]. The underlying mechanism causing this flow has been related to anisotropic turbulent fluctuations. Recently it has been shown through numerical simulations that the flow at transitional Reynolds numbers (\(Re_{b} = \widehat{U}_{b}\widehat{b}/\widehat{v}\), where \(\widehat{U}_{b}\) is the bulk speed, \(\widehat{v}\) the kinematic viscosity and \(\widehat{b}\) the half duct height) can feature instantaneous 4-vortex states (Biau & Bottaro [1] and Uhlmann et al [7]). The lower limit for transition in Re b is between 865 and 1077 [1, 7].
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Wedin, H., Bottaro, A., Nagata, M. (2009). Nonlinear coherent structures in a square duct. In: Eckhardt, B. (eds) Advances in Turbulence XII. Springer Proceedings in Physics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03085-7_35
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DOI: https://doi.org/10.1007/978-3-642-03085-7_35
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