A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures.

Area of Science:

• Fluid dynamics
• Computational mathematics
• Data analysis

Background:

• Lagrangian coherent structures (LCS) are key to understanding fluid flow dynamics.
• Extracting LCS typically involves computationally intensive methods.
• Existing algorithms can be inefficient in terms of time, memory, and output size.

Purpose of the Study:

• To develop a novel ridge tracking algorithm for efficient computation and extraction of LCS.
• To leverage the spatial and temporal coherence of LCS for computational optimization.
• To reduce computational cost and resource requirements for LCS analysis.

Main Methods:

• Developed a ridge tracking algorithm that identifies and follows LCS ridges.
• Utilized spatial coherence by focusing computations on LCS ridges.
• Employed temporal coherence by approximating LCS motion with passive tracer particles.
• Estimated the difference between LCS motion and tracer particle motion.

Main Results:

• The ridge tracking algorithm achieves significant computational speedups, up to 35 times faster than standard methods.
• The algorithm demonstrates reduced memory usage and smaller output file sizes.
• Successfully applied the algorithm to both an analytical double gyre and a simulated swimming jellyfish.

Conclusions:

• The ridge tracking algorithm provides a more efficient approach for computing and extracting LCS.
• The method offers substantial performance improvements over traditional LCS algorithms.
• This technique is applicable to diverse fluid dynamics problems, enhancing analytical capabilities.