Reconstruction of thermally-driven flows using Lagrangian particle data assimilation

Area of Science:

• Fluid Dynamics
• Computational Physics
• Geophysical Science

Background:

• Reconstructing hidden thermal and flow structures from limited observations is a significant challenge.
• Particle trajectories offer valuable but sparse and noisy data for inferring fluid dynamics.

Purpose of the Study:

• To develop and apply a novel four-dimensional variational (4DVar) Marker-in-Cell method.
• To infer comprehensive dynamics of thermally driven flows using particle trajectory data.
• To enable both retrospective reconstruction and forward prediction of convective behavior.

Main Methods:

• Development of a four-dimensional variational (4DVar) Marker-in-Cell method.
• Assimilation of sparse and noisy particle trajectories with governing equations.
• Application to laboratory data for reconstructing temperature fields and predicting future evolution.

Main Results:

• Successful reconstruction of time-dependent temperature fields.
• Inference of the unobservable Rayleigh number, crucial for understanding thermal forcing and heat transport.
• Accurate prediction of future flow evolution beyond the assimilation window, consistent with observations.

Conclusions:

• The 4DVar Marker-in-Cell method provides a robust framework for analyzing thermally or compositionally driven flows.
• The method is effective for both retrospective analysis and forward prediction in geophysical and engineering systems.
• Findings highlight the utility of 4DVar for inferring hidden dynamics from limited observational data.