Turbulence is ubiquitous in hydrodynamics and its study is dominated by statistical methods and dimensional arguments. Even so analytic results tend to rely heavily on statistical symmetries. I will discuss some such results in non-relativistic turbulence and possible extensions to the relativistic case. The 2+1 dimensionality of our numerical setup allows for gaining insight about 3+1 gravity through the fluid/gravity duality. This work aims to further our understanding of the fluid side in its own right. This partly entails determining the robustness of some recently derived relativistic hydrodynamic scaling relations which may have holographic applications.