Influence of tank's length

The Fast Fourier Transform of water level for five various tank's length (first plot) allows to know that the length have an influence on the natural frequency. Thanks to these Fast Fourier Transforms, the natural frequency can be extracted for all the cases and we obtain the second plot.

 

This plot represents the natural frequency (obtained after a fast fourier transform) for five tank's length. Blue points are the Fluent results. A curve fitting returned an inverse function (red points). So the natural frequency is proportional to the inverse of the tank's length : $ f_0 \propto \frac{1}{L} $. Therefore the characteristic length is proportional to the squared of tank's length : $ L^* \propto  L^2 $. 

Thus the characteristic length is proportional to the squared of tank's lenght over the intial water level : 

$ \Rightarrow \displaystyle L^* \propto \frac{L^2}{h} $  

All cases will be ploted in function of this characteristic length in the next part.