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arXiv · 1310.6623

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

Francesco Gargano·Marco Sammartino·Vincenzo Sciacca
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Abstract

We compute the solutions of Prandtl's and Navier-Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl's equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier-Stokes solution at different Reynolds numbers $Re=10^3-10^5$, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers $Re=10^4-10^5$. We also investigate the asymptotic validity of boundary layer theory by comparing Prandtl's solution to Navier-Stokes solutions during the various stages of unsteady separation.

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Francesco Gargano, Marco Sammartino, Vincenzo Sciacca. 2013-10-24. High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex. https://doi.org/10.1016/j.compfluid.2011.08.022

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