A method to statistically characterize turbulent data with physically
  motivated parameters, illustrated on a centroid velocity map
  We investigate the potential of a recently proposed model for 3D compressible
MHD turbulence (Chevillard et al. 2010; Durrive et al. 2021) to be used as a
tool to characterize statistically 2D and 3D turbulent data. This model is
parametrized by a dozen of free (intuitive, physically motivated) parameters,
which control the statistics of the fields (density, velocity and magnetic
fields). The present study is a proof of concept study: (i) we restrict
ourselves to the incompressible hydrodynamical part of the model, (ii) we
consider as data centroid velocity maps, and (iii) we let only three of the
free parameters vary (namely the correlation length, the Hurst parameter and
the intermittency parameter). Within this framework, we demonstrate that, given
a centroid velocity map, we can find in an automated manner (i.e. by a Markov
Chain Monte Carlo analysis) values of the parameters such that the model
resembles the given map, i.e. which reproduces its statistics fairly well.
Hence, thanks to this procedure, one may characterize statistically, and thus
compare, various turbulent data. In other words, we show how this model may be
used as a metric to compare observational or simulated data sets. In addition,
because this model is numerically particularly fast (nearly 500 times faster
than the numerical simulation we use to generate our reference data) it may be
used as a surrogate model. Finally, by this process we also initiate the first
systematic exploration of the parameter space of this model. Doing so, we show
how the parameters impact the visual and the statistical properties of centroid
velocity maps, and exhibit the correlations between the various parameters,
providing new insight into the model.
