Vortex connections at the surface are fundamental and prominent features in free-surface vortical flows. To understand the detailed mechanism of such connection, we consider, as a canonical problem, the laminar vortex connections at a free surface when an oblique vortex ring impinges upon that surface. We perform numerical simulations of the Navier–Stokes equations with viscous free-surface boundary conditions. It is found that the key to understanding the mechanism of vortex connection at a free surface is the surface layers: a viscous layer resulting from the dynamic zero-stress boundary conditions at the free surface, and a thicker blockage layer which is due to the kinematic boundary condition at the surface. In the blockage layer, the vertical vorticity component increases due to vortex stretching and vortex turning (from the transverse vorticity component). The vertical vorticity is then transported to the free surface through viscous diffusion and vortex stretching in the viscous layer leading to increased surface-normal vorticity. These mechanisms take place at the aft-shoulder regions of the vortex ring. Connection at the free surface is different from that at a free-slip wall owing to the generation of surface secondary vorticity. We study the components of this surface vorticity in detail and find that the presence of a free surface accelerates the connection process. We investigate the connection time scale and its dependence on initial incidence angle, Froude and Reynolds numbers. It is found that a criterion based on the streamline topology provides a precise definition for connection time, and may be preferred over existing definitions, e.g. those based on free-surface elevation or net circulation.

We combine experimental, theoretical and numerical efforts to investigate the turbulent wake far behind a surface ship at model scales. Experimental measurements using digital particle image velocimetry (DPIV) are performed for the wakes of three towed hulls with beam-to-draught ratios b/d = 1, 2, 6. Based on model speed and beam, the Reynolds and Froude numbers are O(103) and O(10−2) respectively. Distinct surface features associated with persistent surface-normal vorticity have been identified, which are characterized by large-scale meandering structures. Both lateral and longitudinal scales of the meandering are quantified, with the former found to increase as b/d decreases and the latter independent of b/d. Based on measurements at multiple horizontal and vertical planes, profiles of the mean flow and fluctuation intensity for each velocity component are obtained. To understand the turbulence transition mechanism, an Orr–Sommerfeld stability analysis (OS) is formulated for the wake flow with free-surface boundary conditions, and solved by using a fourth-order finite-difference scheme. Unstable modes antisymmetric to the wake centre-plane are identified. Consistent with the experimental results, the growth rates of unstable modes increase substantially as b/d decreases, while the dependence of meandering wavelengths on b/d is found to be weak. Finally, we perform direct numerical simulation (DNS) of Navier–Stokes equations for the wake flow. The growth rates of unstable modes agree well with the predictions by OS analysis. Compared with experiments, DNS accurately captures the surface-normal vorticity signatures, the meandering features, as well as statistics of turbulence intensity. We also obtain from DNS a detailed description of enstrophy, turbulence length scales, and vortex structures for the wake flow.