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

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 Re 0.8 and P Re 2.25 for 5 × 10 2 ≤ Re ≤ 2 × 10 4 and Z Re 0.5 and P Re 1.5 for Re ≥ 2 × 10 4 (with Re based on the velocity and size of the dipole). A critical Reynolds number Re c (here, Re c≈2 × 10 4) 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 rm Re 3/4, P Re 9/4 and dP/dt Re 11/4 in agreement with the numerically obtained scaling laws. For Re ≥ Re c 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 Re 1/2 and P Re 3/2. © 2010 The Author(s).