A numerical study of laminar to turbulent evolution and free-surface interaction of a vortex ring

Abstract

Direct numerical simulation was used to study various aspects of vortex ring evolution and interaction with a free surface. An investigation of a single unbounded vortex ring at various Reynolds numbers and core thicknesses showed qualitative differences between the evolution of thin- and thick-core rings, leading to a correction factor to the classical equation for the ring translational velocity. The obtained linear modal growth rates were compared 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.

The orthogonal interaction of laminar, transitional and turbulent rings with an initially undisturbed free surface was investigated. At small depths, the expanding ring is unstable to the Crow instability but its dominant mode is predetermined by the prior development of the Widnall instability. The presence of opposite-signed vorticity, due to surface curvature, affects the ring dynamics at the surface. The interaction of a transitional ring modifies the surface displacements, reflecting the structure of the ring below. The secondary structure associated with a transitional ring reconnects to the surface in addition to the inner core. In the presence of the surface, the turbulent ring finds greater coherency of the core due to stretching and aligning of vorticity filaments. The addition of a planar surface wave field modified the ring interaction greatly due to the higher surface curvature and associated surface vorticity. The ring expands asymmetrically and even rebounds locally if sufficient opposite-signed vorticity is generated. The ring diffracts the surface wavefield and the generation of secondary small-amplitude waves was noted.

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