A Lagrangian approach to identifying vortex pinch-off

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics

Background:

• Vortex ring pinch-off is a critical phenomenon in fluid dynamics.
• Existing methods for identifying pinch-off, such as circulation criteria, have limitations, especially in complex flows.

Purpose of the Study:

• To propose and validate a novel criterion for identifying vortex ring pinch-off using Lagrangian Coherent Structures (LCSs).
• To compare the LCS criterion with existing methods and assess its robustness and insights.

Main Methods:

• Demonstration of the LCS criterion in a piston-cylinder flow with an L/D ratio of approximately 12.
• Analysis of LCS behavior, including appearance, termination, and growth, to signify pinch-off initiation and vortex core formation.
• Comparison of LCS-derived formation numbers with established circulation criteria and other flow metrics.

Main Results:

• The appearance and termination of LCSs reliably indicate vortex ring pinch-off initiation.
• The calculated formation number (4.1+/-0.1) closely matches predictions from Gharib et al.
• The LCS approach provides unique insights into vortex pairing in the trailing shear layer, surpassing other methods.

Conclusions:

• The proposed LCS criterion is a robust and objective tool for identifying vortex ring pinch-off.
• This method offers advantages over traditional vorticity-based techniques, particularly for unsteady and low Reynolds number flows.
• LCS analysis enhances understanding of vortex dynamics, including core formation and vortex pairing.