  This study introduces a new family of volumetric flatness factors which give
a rigorous parametric description of the phenomenon of intermittency in fully
developed turbulent flows. These quantities gather information about the most
"active" part of a velocity field at each scale $\ell$, and allows one to
define a dimension function $p \to D_p$ that recovers intermittency correction
to the structure exponents $\zeta_p$ in an explicit way. In particular, the
predictions of the Frisch-Parisi multifractal formalism can be recovered in a
systematic and rigorous way.
  Within this framework we identify active regions that carry the most
energetic part of a velocity field at a given scale $\ell$. A threshold for
what constitutes to be active is defined explicitly. Active regions have proven
to be experimentally observable in our previous joint work \cite{Ph-paper}, and
shown to capture concentration of the energy cascade as $\ell \to 0$, in
\cite{CS2014}.
  We present several examples of fields which exhibit arbitrary multifractal
spectrum within theoretically permitted limitations. At the same time we
demonstrate with the use of a probabilistic argument that a random field is
expected to produce the classical K41 spectrum in the limit $\ell\to 0$.
Intermittent deviations from K41 theory are estimated at any finite scale also.
  Lastly, we present a detailed information-theoretic analysis of the
introduced objects. In particular, we quantify concentration of a given
source-field in terms of the volume factors, thresholds, and active regions.
