What are the structures of Reynolds, Rossby and Ekman numbers in geostrophic turbulence?

To answer that question, I used a shallow water model, chose a resolution sufficiently high in order to simulate a wide range of eddies and computed for a single time step the norm of the advective terms adv, coriolis terms cor and diffusion terms diff (biharmonic mixing is applied in the model) for each grid cell. What you see is

    Re = adv / diff
    Ro = adv / cor
    Ek = diff / cor

in log-scale. One day I want to make an art series of that...