Direct numerical simulation is used to study the temporal development of single vortex rings at various Reynolds numbers and core thicknesses. Qualitative differences between the evolution of thin-and thick-core rings are observed leading to a correction factor to the classical equation for the ring translational velocity. We compare the obtained linear modal growth rates with previous work, highlighting the role of the wake in triply periodic numerical simulations. The transition from a laminar to a turbulent ring is marked by the rearrangement of the outer core vorticity into a clearly defined secondary structure. The onset of the fully turbulent state is associated with shedding of the structure in a series of hairpin vortices. A Lagrangian particle analysis was performed to determine the ring entrainment and detrainment properties and to investigate the possibility of an axial flow being generated around the circumference of the core region prior to the onset of turbulence.

Direct numerical simulation is used to study the development of a single laminar vortex ring as it impinges on a free surface directly from below. We consider the limiting case in which the Froude number approaches zero and the surface can be modelled with a stress-free rigid and impermeable boundary. We find that as the ring expands in the radial direction close to the surface, the natural Tsai–Widnall–Moore–Saffman (TWMS) instability is superseded by the development of the Crow instability. The Crow instability is able to further amplify the residual perturbations left by the TWMS instability despite being of differing radial structure and alignment. This occurs through realignment of the instability structure and shedding of a portion of its outer vorticity profile. As a result, the dominant wavenumber of the Crow instability reflects that of the TWMS instability, and is dependent upon the initial slenderness ratio of the ring. At higher Reynolds number a short-wavelength instability develops on the long-wavelength Crow instability. The wavelength of the short waves is found to vary around the ring dependent on the local displacement of the long waves.

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