Can the wave function show turbulence?

[sgphysics]

I remember from my physics classes that the wave functions for the hydrogen atoms or an electron in a box showed typical linear wave behaviour. However, when you have a large system's wave function, say for example the universe, will it then show different spatial-dynamic structure? What comes to my mind here is some kind of turbulent behaviour or structure.

 

[hilbert2]

If you have a large enough fluid system to be considered macroscopic, its large scale behavior can obey nonlinear effective equations of motion (making turbulence possible), despite the behavior of the atomic constituents being described with linear equations.