There are several reasons turbulence had boggled the brightest minds in physics, math, and engineering for over a century. Physically turbulence extends over many length scales - think of a waterfall for example. All of the kinetic energy gained from the fall must go somewhere and it turns out that somewhere is heat (and sound, but mostly heat). But to turn kinetic energy in a fluid like water into heat, one needs viscosity. In a waterfall, viscosity is effective at dissipating heat through motions on the order of 1 micron. So to understand the turbulence in a waterfall that is something like 10 meters high one needs to understand every micron of the way. On top of that turbulence is chaotic (in the technical sense of the word), meaning that it is essentially random and unpredictable. As an example, take this visualization of jet of fluid entering a super-sonic flow.
There are other reasons turbulence is a really hard problem, but it turns out that what we call the "range of scales" problem is where thinking in terms of sizes makes more sense than thinking in terms of physical position. For you math-junkies out there, that means an integral transform to either Fourier space (for things in boxes) or spherical harmonic space (for spheres). Either way, when you compute the amount of power at each size-scale in the flow, you get a plot that looks like this for the turbulent magnetic field in the solar wind:
...or this for water in tidal channels:
... or this for simulations of solar convection:
