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

Tanner D Harms1, Steven L Brunton2, Beverley J McKeon3

  • 1Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91106, USA.

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This study introduces a new Lagrangian method using regression to estimate flow gradients from sparse tracer data. This approach overcomes limitations of traditional gradient-based techniques for complex dynamical systems.

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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.