Abstract <p>Simultaneous measurement of free-surface deformation and subsurface velocity field is essential for quantitative investigation of vortex–surface interaction, but remains difficult because optical interference near the interface contaminates underwater volumetric velocimetry. In the present study, a simultaneous measurement framework is established for resolving free-surface deformation and subsurface vortex evolution during the head-on impact of a vortex ring (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Re_{\Gamma }=2509$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi mathvariant="normal">Γ</mi> </msub> <mo>=</mo> <mn>2509</mn> </mrow> </math></EquationSource> </InlineEquation>) with an air–water interface. Stereoscopic surface measurement and four-dimensional particle tracking velocimetry (4D-PTV) are integrated within a common spatial coordinate system and synchronized time base, enabling time-resolved capture of the coupled interface and subsurface flow dynamics. The feasibility of the system relies on three strategies: dual illumination with optical filtering to separate free-surface and underwater particle images, short-time-window background subtraction to suppress surface reflection, and temporal continuity in Lagrangian tracking to identify valid underwater particle trajectories. The synchronized measurements resolve the full interaction process and quantify the vortex–surface response in different evolution stages through circulation, kinetic energy within the vortex core region, and free-surface energy evolution. The dataset quality is supported by three independent checks: a kinematic boundary condition residual sharply concentrated near zero, with a three-sigma level of 0.65% of the characteristic vortex velocity; a stress-free-consistency indicator that remains low overall, with localized peaks restricted to strong vortex–surface interaction regions; and a correlation-based time lag analysis showing physically consistent upward propagation of vortex-induced disturbances before direct impact. The present framework therefore provides an experimental solution for linking subsurface vortical dynamics to free-surface response in a time-resolved and spatially registered manner.</p> Graphical abstract <p></p>

Simultaneous free-surface and 3D flow measurements of a vortex ring in head-on collision with the air–water interface

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发表日期：

2026年6月27日

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Yukun Han,
Jinho Oh,
Chong Pan,
Sang Youl Yoon,
Kyung Chun Kim

摘要

Abstract

Simultaneous measurement of free-surface deformation and subsurface velocity field is essential for quantitative investigation of vortex–surface interaction, but remains difficult because optical interference near the interface contaminates underwater volumetric velocimetry. In the present study, a simultaneous measurement framework is established for resolving free-surface deformation and subsurface vortex evolution during the head-on impact of a vortex ring ( $Re_{\Gamma }=2509$ $R e_{Γ} = 2509$ ) with an air–water interface. Stereoscopic surface measurement and four-dimensional particle tracking velocimetry (4D-PTV) are integrated within a common spatial coordinate system and synchronized time base, enabling time-resolved capture of the coupled interface and subsurface flow dynamics. The feasibility of the system relies on three strategies: dual illumination with optical filtering to separate free-surface and underwater particle images, short-time-window background subtraction to suppress surface reflection, and temporal continuity in Lagrangian tracking to identify valid underwater particle trajectories. The synchronized measurements resolve the full interaction process and quantify the vortex–surface response in different evolution stages through circulation, kinetic energy within the vortex core region, and free-surface energy evolution. The dataset quality is supported by three independent checks: a kinematic boundary condition residual sharply concentrated near zero, with a three-sigma level of 0.65% of the characteristic vortex velocity; a stress-free-consistency indicator that remains low overall, with localized peaks restricted to strong vortex–surface interaction regions; and a correlation-based time lag analysis showing physically consistent upward propagation of vortex-induced disturbances before direct impact. The present framework therefore provides an experimental solution for linking subsurface vortical dynamics to free-surface response in a time-resolved and spatially registered manner.

Graphical abstract