  In this work, single particle dispersion was analyzed for a bacterial
turbulence by retrieving the virtual Lagrangian trajectory via numerical
integration of the Lagrangian equation. High-order displacement functions were
calculated for cases with and without mean velocity effect. Two-regime
power-law behavior for short and long time evolutions were identified
experimentally, which were separated by the Lagrangian integral time. For the
case with the mean velocity effect, the experimental Hurst numbers were
determined to be $0.94$ and $0.97$ for short and long times evolutions,
respectively. For the case without the mean velocity effect, the values were
$0.88$ and $0.58$. Moreover, very weak intermittency correction was detected.
All measured Hurst number were above $1/2$, the value of the normal diffusion,
which verifies the super-diffusion behavior of living fluid. This behavior
increases the efficiency of bacteria to obtain food.
