  In this paper, an experimental velocity database of a bacterial collective
motion , e.g., \textit{B. subtilis}, in turbulent phase with volume filling
fraction $84\%$ provided by Professor Goldstein at the Cambridge University UK,
was analyzed to emphasize the scaling behavior of this active turbulence
system. This was accomplished by performing a Hilbert-based methodology
analysis to retrieve the scaling property without the $\beta-$limitation. A
dual-power-law behavior separated by the viscosity scale $\ell_{\nu}$ was
observed for the $q$th-order Hilbert moment $\mathcal{L}_q(k)$. This
dual-power-law belongs to an inverse-cascade since the scaling range is above
the injection scale $R$, e.g., the bacterial body length. The measured scaling
exponents $\zeta(q)$ of both the small-scale \red{(resp. $k>k_{\nu}$) and
large-scale (resp. $k<k_{\nu}$)} motions are convex, showing the
multifractality. A lognormal formula was put forward to characterize the
multifractal intensity. The measured intermittency parameters are $\mu_S=0.26$
and $\mu_L=0.17$ respectively for the small- and large-scale motions. It
implies that the former cascade is more intermittent than the latter one, which
is also confirmed by the corresponding singularity spectrum $f(\alpha)$ vs
$\alpha$. Comparison with the conventional two-dimensional Ekman-Navier-Stokes
equation, a continuum model indicates that the origin of the multifractality
could be a result of some additional nonlinear interaction terms, which
deservers a more careful investigation.

Fluid Dynamics;Biological Physics