Interaction of an obliquely rising vortex ring with a free surface in a viscous fluid

Ohring, Samuel; Lugt, Hans J.

doi:10.1007/bf00426971

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…These features are expected to be more prominent in flows with higher Froude numbers (i.e. larger surface deformations) such as numerically simulated by Ohring & Lugt (1995), for example.…”

Section: Flux Of Vorticity At the Free Surfacementioning

confidence: 93%

Experimental studies of vortex disconnection and connection at a free surface

Gharib

Weigand

1996

J. Fluid Mech.

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An experimental study is presented that examines the interaction of a vortex ring with a free surface. The main objective of this study is to identify the physical mechanisms that are responsible for the self-disconnection of vortex filaments in the near-surface region and the subsequent connection of disconnected vortex elements to the free surface. The understanding of those mechanisms is essential for the identification and estimation of the appropriate spatial and temporal scales of the disconnection and connection process. In this regard, the velocity and vorticity fields of an obliquely approaching laminar vortex ring with a Reynolds number of 1150 were mapped by using Digital Particle Image Velocimetry (DPIV). The evolution of the near-surface vorticity field indicates that the connection process starts in the side regions of the approaching vortex ring where surface-normal vorticity already exists in the bulk. A local strain rate analysis was conducted to support this conclusion. Disconnection in the near-surface tip region of the vortex ring occurs because of the removal of surfaceparallel vorticity by the viscous flux of vorticity through the surface. Temporal and spatial mapping of the vorticity field at the surface and in the perpendicular plane of symmetry shows that the viscous flux is balanced by a local deceleration of the flow at the surface. It is found that the observed timescales of the disconnection and connection process scale with the near-surface vorticity gradient rather than with the core diameter of the vortex ring.

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“…These features are expected to be more prominent in flows with higher Froude numbers (i.e. larger surface deformations) such as numerically simulated by Ohring & Lugt (1995), for example.…”

Section: Flux Of Vorticity At the Free Surfacementioning

confidence: 93%

Experimental studies of vortex disconnection and connection at a free surface

Gharib

Weigand

1996

J. Fluid Mech.

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“…In this article, we provide a transport equation for the surface-normal vorticity in the interface or free surface, which relates the appearance of surface-normal vorticity in the surface to the viscous diffusion of surface-tangential vorticity across the boundary. In particular, this leads to a new interpretation of vortex connection to a free surface, where vortex filaments are broken near the free surface, and the ends of these filaments attach to the free surface (Bernal & Kwon 1989; Lugt & Ohring 1994; Gharib & Weigand 1996; Ohring & Lugt 1996; Zhang, Shen & Yue 1999). Under the interpretation proposed in this paper, the appearance of surface-normal vorticity in the free surface is directly attributed to the viscous flux of surface-tangential vorticity out of the fluid.…”

Section: Introductionmentioning

confidence: 99%

Vorticity generation and conservation on generalised interfaces in three-dimensional flows

2022

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This article presents a three-dimensional theory of vorticity creation on generalised interfaces, including both non-slip and free-slip boundaries, which generalises a previous two-dimensional formulation (Terrington et al., J. Fluid Mech., vol. 890, 2020, p. A5). Under this description, vorticity may be created on a boundary by the inviscid relative acceleration between fluid elements on each side of the boundary, driven by either tangential pressure gradients or body forces. Viscosity acts to transfer circulation between the vortex sheet representing the slip velocity on the interface, and the fluid interior, but is not responsible for the creation of vorticity on the interface. This formulation also describes a principle of vorticity conservation for interfacial and free-surface flows: in many flow configurations, the net generation of vorticity on the interface is zero, and the total circulation remains constant throughout flow evolution.

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“…This problem was also studied experimentally by Willert & Gharib (1997). Simulations for the case of a ring approaching a deformable surface were performed by Lugt & Ohring (1994) and Ohring & Lugt (1996). These simulations provide a more complete picture of the process of free-surface vortex connection.…”

Section: Introductionmentioning

confidence: 99%

The mechanism of vortex connection at a free surface

1999

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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.

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Interaction of an obliquely rising vortex ring with a free surface in a viscous fluid

Cited by 7 publications

References 19 publications

Experimental studies of vortex disconnection and connection at a free surface

Experimental studies of vortex disconnection and connection at a free surface

Vorticity generation and conservation on generalised interfaces in three-dimensional flows

The mechanism of vortex connection at a free surface

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