Influence of the acceleration

A really important factor in this study is the acceleration of the plane. This is the more complicated factor to study because of high accelerations, with which wetting happens.

Firstly, the theoretical dissipation time is proportional to the squared acceleration over the squared gravity : $ T^2 \propto \frac{a^2}{g^2} $.  From the plot, the dissipation time is larger for the high acceleration (blue curve). There is a contradiction with the theory.

In fact, $ T_{blue curve_ {th}} \approx 10^{4} s $ and $ T_{blue curve_{plot}} \approx 50 s $

But in this case (high acceleration), wetting happens. The following drawing shows the free surface form : 

We try to imagine a new case : we take the same tank turned of 90 degrees and we reverse the acceleration and the gravity : 

We obtain a new dissipation time : $ T'_{blue curve_{th}} = 500 s $. This result is closer but it is not exact. 

 

$\Rightarrow$ To conclude this part about dissipation time, its theoretical expression is correct without wetting.