Turbulence in the vicinity of black holes represents a poorly understood, very complex challenge. We propose a novel analysis technique for the comprehension of turbulence in extreme gravitational fields, such as the ergosphere of compact objects. We develop a turbulence measurement that, in principle, can be valid in any curved spacetime. In a fully covariant formalism, taking into account the local spatial metric of Kerr-type black holes, we define a Proper Length Spectrum (PLS). We demonstrate that the new technique, based on the computation of structure functions on generic manifolds, can correctly capture the scaling laws indicative of an inertial range cascade. By applying the PLS to the turbulent density field coming from simulations of the Black Hole Accretion Code, we estimate the scaling laws of turbulence in the disk, the wind, and the near-horizon regions.
