Describing turbulent fluid flows remains challenging, despite massive computational resources being devoted to it. This is because turbulent fluids interact on a vast range of spatial and temporal scales and the dynamics is sensitive to small disturbances. In particular, prediction of such systems remains difficult. In many cases, though the models are imperfect, more faithful predictions can be achieved by combining the models with observations of the system. This observational knowledge can then be assimilated into the model to provide better predictive capability, and also to estimate the parameters of an uncertain model. This study aims to test the capabilities of one such assimilation scheme, the Ensemble Kalman Filter (EnKF), in aiding the prediction of the complex behaviour in a thermal rotating annulus.
Four results are presented in this thesis. First, EnKF was applied to the Lorenz model, where tests were performed with varying ensemble sizes, inflation, and gaps between data assimilation. This was to understand the limitations of EnKF on a smaller chaotic system. It was determined that only a small ensemble size of just 7 was required to accurately predict model behaviour. Tests were also done on EnKF capabilities on parameter estimation where the system predicted the values of the parameters very accurately.
Second, the experimental results are presented for thermal rotating annulus experiments which were done at a velocity of 1\,rad/s, 2.5\,rad/s and 3\,rad/s. The experiments showed behaviour that is expected at the various rotation rates. We found that it was difficult to get accurate results for behaviour at the lower levels of the annulus compared to data at higher levels. Overall the one size fits all approach to the PIV settings for analysing images does not seem to work well and future studies will have to fine tune the setting for more accurate analysis.
Third, a twin experiment where EnKF was performed using the MORALS code with a high resolution `truth' and low resolution ensemble. Studies were done at 1\,rad/s, 2\,rad/s, 2.5\,rad/s and 3\,rad/s. At 1\,rad/s, EnKF did a good job of tracking the `truth' at different settings. Looking at 2\,rad/s, in most cases the low resolution ensemble system struggled to replicate the m=4 wavenumber observed in the `truth' and stayed at m=3 wavenumber. Although decreasing the DA length to every 1 minute gave the best result, in many cases the system strayed away from the truth. Going further to 2.5\,rad/s, the structures observed at this rotation rate were very volatile with the system finding it hard to track the truth. This was the case even when the time between DA was decreased or the ensemble size increased. Lastly at 3\,rad/s the low resolution models in the ensemble always gave the wrong wavenumber and was not able to track the truth. It seems that the resolution for the ensemble needs to be increased for better simulation at higher rotation rates.
Finally, the results for using low resolution ensemble MORALS to predict experimental results were presented where tests were done at 1\,rad/s and 2.5\,rad/s. At 1rad/s the ensemble can replicate the fluid structures observed in the PIV data with an m=3 wave but the ensemble was never able to tack the `truth' with the latter travelling around the annulus faster. At a higher rotation rate of 2.5rad/s the ensemble is never able to replicate the m=4 wave as observed in the `truth'. This is even the case when the $\theta$ resolution is increased to 128 points.
From the results presented in this thesis EnKF can be seen as a reasonable solution to help predict behaviour in a thermal rotating annulus setting. It does a good job of giving close results to the truth in most of the twin studies. And although there were problems when using the experimental results there should be improvement in the results when better analysis techniques are used to obtain better observations. EnKF overall has problems at higher rotation rates this problem can also be overcome using different settings in the ensemble and EnKF.
