I finally found a study where they experimented with the height of the enclosure.
A further increase in the tube height results in the oscillation of the candle flame which is explained as follows. When the flame is at its peak, there is insufficient incoming ambient air (and hence oxygen) to burn, and its length is reduced. A smaller flame allows more ambient air which causes the flame height to increase. This pattern keeps repeating itself and hence the observed oscillations in the flame size.
Conclusion
The behaviour of a candle flame, with the candle placed in a tube open at the top and closed at the bottom, was studied with varying tube heights. The novelty of the current configuration is that the air required for combustion can only enter the tube from the top since the tube bottom is sealed. It was observed that when the tube height was increased, the flame changed its behaviour from fluttering to steady state burning, to oscillation, and finally to it being extinguished rapidly.