On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

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Keetels, G.H. and Kramer, W. and Clercx, H.J.H. and Heijst, G.J.F. van (2011) On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions. Theoretical and computational fluid dynamics, 25 (5). pp. 293-300. ISSN 0935-4964

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Abstract:Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z ∝ Re0.8 and P ∝ Re2.25 for 5 × 102 ≤ Re ≤ 2 × 104 and Z ∝ Re0.5 and P ∝ Re1.5 for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Rec(here, Rec ≈ 2 × 104) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z ∝ Re^3/4, P ∝ Re^9/4, and dP/dt ∝ Re11/4 in agreement with the numerically obtained scaling laws. For Re ≥ Rec the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z ∝ Re1/2 and P ∝ Re3/2.
Item Type:Article
Copyright:© 2011 Springer
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/79417
Official URL:http://dx.doi.org/10.1007/s00162-010-0205-7
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