Objective Lagrangian Vortex Cores and their Visual Representations

Area of Science:

• Fluid Dynamics
• Computational Science

Background:

• Vortex core extraction is crucial for analyzing time-dependent fluid flows.
• Existing methods struggle to satisfy both objectivity and Lagrangian constraints for vortex corelines.
• A guaranteed Lagrangian property for vortex corelines remains an open challenge.

Purpose of the Study:

• To propose the first vortex core definition that is both objective and Lagrangian.
• To develop a method ensuring vortex corelines are true pathlines of the fluid flow.
• To enable accurate visualization of vortex cores in 2D and 3D time-dependent flows.

Main Methods:

• Restricting observer motion to pathlines to reduce degrees of freedom.
• Optimizing observer rotation to achieve a steady observed flow.
• Calculating vortex deviation error and using gradient descent for sub-voxel accuracy.
• Visualizing vortex cores as pathlines and swirling motion via streamlines.

Main Results:

• Successfully defined objective and Lagrangian vortex corelines.
• Demonstrated that the optimization yields non-zero time-partial derivatives elsewhere.
• Achieved sub-voxel accuracy in coreline extraction using gradient descent.
• Validated the approach on various 2D and 3D time-dependent vector fields.

Conclusions:

• The proposed method provides the first formally objective and Lagrangian vortex core definition.
• This approach accurately identifies vortex corelines as pathlines in complex flows.
• The technique offers improved visualization and analysis of vortical structures in fluid dynamics.