English

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

Mathematical Physics 2013-10-25 v1 Analysis of PDEs math.MP Fluid Dynamics

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=103105Re=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=104105Re=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.

Keywords

Cite

@article{arxiv.1310.6623,
  title  = {High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex},
  author = {Francesco Gargano and Marco Sammartino and Vincenzo Sciacca},
  journal= {arXiv preprint arXiv:1310.6623},
  year   = {2013}
}