Vortex ring connection to a free surface

Terrington, S.J.; Hourigan, Kerry; Thompson, Mark C.

doi:10.1017/jfm.2022.529

Cited by 8 publications

(26 citation statements)

References 40 publications

(199 reference statements)

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“…The viscous term in (2.27) describes changes to the surface-normal vorticity that occur as a consequence of the diffusion of surface-tangential vorticity across the boundary. We have previously shown that this representation clearly illustrates how the kinematic condition that vortex lines do not end in the fluid is maintained (Terrington et al 2021(Terrington et al , 2022bTerrington, Hourigan & Thompson 2022a). For example, in the case of vortex ring connection to a free surface (Terrington et al 2022a), the diffusion of tangential vorticity out of the fluid (breaking open of vortex lines) coincides with the appearance of new surface-normal vorticity in the free surface (attachment of vortex lines to the boundary).…”

Section: Boundary Conditions For Surface-normal Vorticitymentioning

confidence: 75%

“…For the oblique interaction between a vortex ring and a flat free-slip wall (Balakrishnan, Thomas & Coleman 2011), or a clean free surface Song et al 1991;Lugt & Ohring 1994;Gharib & Weigand 1996;Ohring & Lugt 1996;Zhang, Shen & Yue 1999;Terrington et al 2022a), a phenomenon known as vortex connection occurs. Surface-tangential vorticity from the upper part of the vortex ring diffuses out of the fluid at the free-slip boundary, causing the vortex ring to open up and attach to the surface.…”

Section: Vortex Ring Interactions With a Partial-slip Boundarymentioning

confidence: 99%

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Vorticity dynamics at partial-slip boundaries

Terrington,

Thompson,

Hourigan

2024

J. Fluid Mech.

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In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased.

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Section: Boundary Conditions For Surface-normal Vorticitymentioning

confidence: 75%

Section: Vortex Ring Interactions With a Partial-slip Boundarymentioning

confidence: 99%

Vorticity dynamics at partial-slip boundaries

Terrington,

Thompson,

Hourigan

2024

J. Fluid Mech.

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“…Finally, the L–H interpretation clearly illustrates how the kinematic condition that vortex lines do not end inside the fluid is maintained during viscous processes such as vortex reconnection (Terrington et al. 2021), or the connection of a vortex ring to a free surface (Terrington, Hourigan & Thompson 2022 a ). In addition, Eyink (2021) has shown that the Huggins tensor leads to a generalised Josephson–Anderson relation between the drag on a finite solid body and the vorticity flux.…”

Section: Enstrophy Dynamicsmentioning

confidence: 99%

“…2021), and for the interaction between a vortex ring and a free surface (Terrington et al. 2022 a ). Even if the L–H and L–P interpretations of enstrophy dynamics are quantitatively similar for highly inertial flows, only the L–H interpretation of enstrophy dynamics is consistent with the L–H interpretation of vorticity dynamics.…”

Section: Examplesmentioning

confidence: 99%

“…We remark that even for inertially dominated flows, the L-H interpretation still offers several benefits for understanding the dynamics of vorticity. For example, the L-H interpretation has been used to provide an elegant description of the generation and conservation of vorticity in rotating and translating sphere flows (Terrington et al 2021), and for the interaction between a vortex ring and a free surface (Terrington et al 2022a). Even if the L-H and L-P interpretations of enstrophy dynamics are quantitatively similar for highly inertial flows, only the L-H interpretation of enstrophy dynamics is consistent with the L-H interpretation of vorticity dynamics.…”

Section: Stokes Flow Over Rotating Spherementioning

confidence: 99%

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The Lyman–Huggins interpretation of enstrophy transport

Terrington

Hourigan²,

Thompson³

2023

J. Fluid Mech.

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The Lighthill–Panton and Lyman–Huggins interpretations of vorticity dynamics are extended to the dynamics of enstrophy. There exist two competing definitions of the vorticity current tensor, which describes the flow rate of vorticity in the fluid interior, and the corresponding boundary vorticity flux, which represents the local vorticity creation rate on a boundary. It is demonstrated that each definition of the vorticity current tensor leads to a consistent set of definitions for the enstrophy current, boundary enstrophy flux and the enstrophy dissipation term. This leads to two alternative interpretations of vorticity and enstrophy dynamics: the Lighthill–Panton and Lyman–Huggins interpretations. Although the kinematic evolution of the vorticity and enstrophy fields are the same under each set of definitions, the dynamical interpretation of the motion generally differs. For example, we consider the Stokes flow over a rotating sphere, and find that the flow approaches a steady state where, under the Lyman–Huggins interpretation, there is no enstrophy creation or dissipation. Under the Lighthill–Panton interpretation, however, the steady-state flow features a balance between the continuous generation and subsequent dissipation of enstrophy. Moreover, the Lyman–Huggins interpretation has previously been shown to offer several benefits in understanding the dynamics of vorticity, and therefore it is beneficial to extend this interpretation to the dynamics of enstrophy. For example, the Lyman–Huggins interpretation allows the creation of vorticity, and therefore enstrophy, to be interpreted as an inviscid process, due to the relative acceleration between the fluid and the boundary.

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