Lagrangian gradient regression for the detection of coherent structures from sparse trajectory data.

Area of Science:

• Fluid dynamics
• Dynamical systems theory
• Data-driven modeling

Background:

• Lagrangian coherent structures (LCS) are key to analyzing complex flows using tracer motion.
• Traditional LCS methods often require accurate flow gradients, which are difficult to compute from sparse observational data like ocean drifters.
• Existing methods for sparse data do not fully capture gradient information.

Purpose of the Study:

• To develop a purely Lagrangian, data-driven method for computing instantaneous and finite-time flow gradients.
• To address the challenge of estimating flow gradients from sparse trajectory data.

Main Methods:

• A novel regression-based approach is proposed to estimate flow gradients directly from sparse tracer trajectories.
• The method is demonstrated on an analytical benchmark to illustrate its functionality and performance.

Main Results:

• The proposed method effectively estimates flow gradients even with sparse data, mimicking real-world observational limitations.
• It provides a viable alternative to traditional gradient-computation methods in data-scarce scenarios.

Conclusions:

• This data-driven Lagrangian technique offers a powerful new tool for analyzing complex flows and dynamical systems where gradient computation is challenging.
• It enhances the applicability of LCS theory to systems with limited observational data.