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The active role of vorticity in the collision of a Lamb-like dipole with a no-slip wall is studied for Re values ranging between 625 and 20000. The initial approach of the dipole does not differ from the stress-free case or from a point-vortex model that incorporates the diffusive growth of the dipole core. When closer to the wall, the detachment and subsequent roll-up of the boundary layer leads to a viscous rebound, as was observed by Orlandi ͓Phys. Fluids A 2, 1429 ͑1990͔͒ in numerical simulations with Re up to 3200. The net translation of the vortex core along the wall is strongly reduced due to the cycloid-like trajectory. For Reഛ 2500 wall-generated vorticity is wrapped around the separate dipole halves, which hence become ͑partially͒ shielded monopoles. For Reտ O͑10 4 ͒, however, a shear instability causes the roll-up of the boundary layer before it is detached from the wall. This leads to the formation of a number of small-scale vortices, between which intensive, narrow eruptions of boundary-generated vorticity occur. Quantitative measures are given for the influx of vorticity at the wall and the consequent increase of boundary layer vorticity and enstrophy.

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 ∝ 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 .

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This paper reports on a numerical study of forced two-dimensional turbulence in a periodic channel with flat no-slip walls. Since corners or curved domain boundaries, which are met in the standard rectangular, square, or circular geometries, are absent in this geometry, the (statistical) analysis of the flow is substantially simplified. Moreover, the use of a standard Fourier–Chebyshev pseudospectral algorithm enables high integral-scale Reynolds number simulations. The paper focuses on (i) the influence of the aspect ratio of the channel and (ii) the integral-scale Reynolds number on the large-scale self-organization of the flow. It is shown that for small aspect ratios, a unidirectional flow spontaneously emerges, notably in the absence of a pressure gradient in the longitudinal direction. For larger aspect ratios, the flow tends to organize into an array of counter-rotating vortical structures. The computed energy and enstrophy spectra provide further evidence that the injection of small-scale vorticity at the no-slip walls modify the inertial-range scaling. Additionally, the quasistationary final state of decaying turbulence is interpreted in terms of the Stokes modes of a viscous channel flow. Finally, the transport of a passive tracer material is studied with emphasis on the role of the large-scale flow on the dispersion and the spectral properties of the tracer variance in the presence of no-slip boundaries.