Assimilation of nearly turbulent Rayleigh-B\'enard flow through vorticity or local circulation measurements: a computational study

TL;DR

This study develops a data assimilation algorithm for 2D Bénard convection that effectively reconstructs flow fields using only coarse vorticity measurements, demonstrating convergence beyond theoretical expectations.

Contribution

Introduces a novel continuous data assimilation method for 2D Bénard convection using vorticity measurements, achieving convergence with coarser data than previously established.

Findings

Algorithm converges to true flow solutions using coarse vorticity data.

Convergence occurs even with data resolution coarser than theoretical predictions.

Method effectively reconstructs temperature and vorticity fields in simulations.

Abstract

We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to constrain the model. Our numerical results indicate that the approximate solution of the algorithm is converging to the unknown reference solution (vorticity and temperature) corresponding to the measurements of the 2D B\'enard convection problem when only spatial coarse-grain measurements of vorticity are assimilated. Moreover, this convergence is realized using data which is much more coarse than the resolution needed to satisfy rigorous analytical estimates.