The fundamental equations that model turbulent flow do not provide much
insight into the size and shape of observed turbulent structures. We
investigate the efficient and accurate representation of structures in
two-dimensional turbulence by applying statistical models directly to the
simulated vorticity field. Rather than extract the coherent portion of the
image from the background variation, as in the classical signal-plus-noise
model, we present a model for individual vortices using the non-decimated
discrete wavelet transform. A template image, supplied by the user, provides
the features to be extracted from the vorticity field. By transforming the
vortex template into the wavelet domain, specific characteristics present in
the template, such as size and symmetry, are broken down into components
associated with spatial frequencies. Multivariate multiple linear regression is
used to fit the vortex template to the vorticity field in the wavelet domain.
Since all levels of the template decomposition may be used to model each level
in the field decomposition, the resulting model need not be identical to the
template. Application to a vortex census algorithm that records quantities of
interest (such as size, peak amplitude, circulation, etc.) as the vorticity
field evolves is given. The multiresolution census algorithm extracts coherent
structures of all shapes and sizes in simulated vorticity fields and is able to
reproduce known physical scaling laws when processing a set of voriticity
fields that evolve over time