I guess differential equations are pretty bad at solutions that look like noise. So why beat the bush and instead define a new category of methods. Call them Intensity Equations or something similar.
So then something like violent turbulence could be ?solved by formulating an intensity equation.
Maybe the solutions is not possible to get by hand since the amount of information in the information dense picture of the real world sample is pretty large.
So the intensity equation should ?with the help of a generator, G(noise) create an information dense solution.