Predicting flow reversals in chaotic natural convection using data assimilation

ABSTRACT

A simplified model of natural convection, similar to the Lorenz system, is compared to computational fluid dynamics simulations of a thermosyphon in order to test data assimilation (DA) methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference ‘truth’. Forecasts are then made using the Lorenz-like model and synchronised to noisy and limited observations of the truth using DA. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows. Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals.

• chaos
• data assimilation
• forecasting
• Lorenz system
• thermosyphon

6. Acknowledgements

We would like to thank Dennis Clougherty, Peter Dodds, Nicholas Allgaier and Ross Lieb-Lappen for their comments and discussion and the three anonymous reviewers for providing many comments and suggestions that strengthened the paper. We also thank Shu-Chih Yang for providing 3-D-Var MATLAB code, which was used to prototype our own experiments. We also wish to acknowledge financial support from the Vermont Space Grant Consortium, NASA EPSCoR, NSF-DMS Grant No. 0940271, the Mathematics & Climate Research Network and the Vermont Advanced Computing Center.