Level set formulation of two-dimensional Lagrangian vortex detection methods.

Area of Science:

• Fluid dynamics
• Computational mathematics
• Applied physics

Background:

• Identifying vortex boundaries is crucial for understanding fluid flow dynamics.
• Previous methods often struggle with capturing multiple vortices simultaneously or require significant computational resources.

Purpose of the Study:

• To develop and demonstrate a novel variational level set methodology for capturing Lagrangian vortex boundaries in 2D unsteady velocity fields.
• To offer a computationally efficient approach for identifying vortex structures based on different coherence principles.

Main Methods:

• The study employs the variational level set methodology, reformulating vortex boundary detection as an optimization problem.
• Two distinct variational formulations are utilized: one based on piecewise uniform stretching and another on a graph-based approach.
• The level-set formulation allows for the simultaneous capture of an arbitrary number of vortices.

Main Results:

• The proposed level-set method successfully identifies Lagrangian vortex boundaries in various 2D unsteady velocity fields.
• The technique demonstrates effectiveness for both proposed variational formulations, capturing vortices based on different coherence definitions.
• The method achieves this identification at a relatively low computational cost.

Conclusions:

• The variational level set methodology provides an efficient and robust tool for Lagrangian vortex boundary detection in fluid dynamics.
• This approach offers flexibility by accommodating different mathematical definitions of vortex coherence.
• The technique has the potential for broad application in analyzing complex fluid flow phenomena.