# Wind Reversal in Bubbly Natural Convection
## 3 Results  
### Convection Enhancement Induced by Vapor Bubbles Nucleation  
The control parameter quantifying the convection is the time evolution of the Nusselt number \(Nu\) (heat flux transferred through the plates normalized by its purely conductive value) as shown in Figure 1. No bubbles flow manifested itself with a single roll that fills the whole domain and the Nusselt number shows a stationary behavior with a constant value equal to 4.718. Such a laminar flow gets highly non-stationary behavior induced by the dispersion of vapor bubbles nucleated at the bottom plate. The rising motion of bubbles increases the fluid energy in terms of both momentum and heat. Those enhancements of the flow energy flow are function of the Jakob number.  
The Jakob number is a dimensionless parameter that takes into account the bubble ability to increase its own volume due to the heat transfer with the surrounding fluid. To increase the Jakob number, the bubbles enlarge more and more, traveling in the vertical direction towards the upper plate. Under this condition, the presence of bubbles increases the time averaged Nusselt number from 4.718 (no bubble flow) to 13.13 (two-way coupling flow). It should be pointed out that the bubble becoming bigger compared to its initial size changes its dynamics, which can be described by means of the point-like approximation. Moreover, the bubbles are responsible of the fluctuations in time of the Nusselt number, as their irregular rising motion generates small vortical structures characterized by highly non-stationary regime with high frequencies of the control parameter signal.  
The dispersion of bubbles causes a strongly non-linear change in the heat transfer. In Figure 1 two flow cases, with and without bubbles, are shown for a computational domain with aspect ratio \(\Gamma=1/2\). The average value of the heat transfer trend of the flow with bubbles is much enhanced, with respect to non bubble flow and it is worth noting how the fluctuations determined the transition to a turbulent-like behavior. In Figure 1b, the probability density function of the Nusselt number fluctuations is shown  
As we see, the probability density function of Nu nicely agrees with the Gaussian distribution. This statement underline the role played by the rare events of the distribution tail superimposed to the mainstream circulation. The rare events due to the nucleation, growth, and rising motion of the bubbles, are independent because ruled by the Gaussian distribution. The bubbles are not clustered by the flow if we consider the average time at which any random configuration is allowed. Instead, if we look at the instantaneous displacement of the bubbles (Figure 2) they are preferentially located into the ascending stream.  
Figure 1: (**a**) Nusselt number time history number for \(\Gamma=1/2\), \(Ra=2\times 10^{5}\) and \(Pr=1.65\). Solid line indicates the flow without bubbles and the dashed line indicates the two-way coupling case. (**b**) Probability density function (pdf) of the Nusselt number time series compare with the Gaussian distribution.  
How can the bubbles behave differently? The answer is in the wind reversal, which instantaneously pushes the particles to the ascending stream, but also sweeps over the azimuthal direction, and in doing so, avoiding any preferential marker in the average thermodynamical parameters. In fact, they follow the Gaussian distribution such as the Nusselt number.  
The following investigation was based on the evidence that the Nusselt number shows higher frequencies mainly because of small structures induced by the bubbles rather than the large-scale circulation.