In that case, the eddy coefficient is proportional to the local velocity magnitude so that the Reynolds number $Re =\lvert U \rvert e / A_l$ is constant (and here hardcoded to $12$):
\colorbox{yellow}{JC comment: The Reynolds is effectively set to 12 in the code for both operators but shouldn't it be 2 for Laplacian ?}
In that case, the eddy coefficient is proportional to the local velocity magnitude so that the Reynolds number $Re =\lvert U \rvert e / A_l$ is constant (and here hardcoded to $2$ for the Laplacian and $12$ for the Bilaplacian):
\begin{equation}
\label{eq:LDF_flowah}
A_l = \left\{
\begin{aligned}
&\frac{1}{12}\lvert U \rvert e &\text{for laplacian operator }\\
&\frac{1}{2}\lvert U \rvert e &\text{for laplacian operator }\\
&\frac{1}{12}\lvert U \rvert e^3 &\text{for bilaplacian operator }