  This work presents a theoretical investigation of active turbulence in a
dusty plasma monolayer, where energy is injected at the individual particle
level and transported to larger scales, leading to the spontaneous formation of
spatially disordered flow patterns. Many-body simulations of 10,000-particle
dusty plasma monolayers are used to demonstrate how the global dynamics depend
on the statistical properties of the dust assembly for realistic laboratory
conditions. We find that spatial defects due to variations in the dust size
distribution and charge-driven nonlocal interactions resulting in anomalous
dust diffusion, are key factors for the onset of instabilities. The resulting
dynamics exhibits features of inertial turbulence over slightly less than one
decade of scales, down to scales on the order of the particle diameter. These
processes are examined analytically using a recently developed Fractional
Laplacian Spectral (FLS) technique, which identifies the active energy channels
as a function of scale, disorder concentration, and nonlocality. The
predictions from the theoretical (spectral) analysis demonstrate agreement with
the results from the many-body (kinetic) simulations, thus providing a powerful
tool for the study of active turbulence.
