  We simulated a turbulent pipe flow within the Lattice Boltzmann Method using
a multiple-relaxation-time collision operator with Maxwell-Boltzmann
equilibrium distribution expanded, for the sake of a more accurate description,
up to the sixth order in Hermite polynomials. The moderately turbulent flow
($Re_{\tau} \approx 181.3$) is able to reproduce up to the fourth statistical
moment with great accuracy, compared with other numerical schemes and with
experimental data. A coherent structure identification was performed based on
the most energetic streamwise turbulent mode, which revealed a surprising
memory effect related to the large scale forcing scheme used to trigger the
turbulent state in the pipe. We observe that the existence of large scale
motions which are out of the pipe's stationary regime do not affect the
detailed single-point statistical features of the flow. Furthermore, the
transitions between the coherent structures of different topological modes were
analyzed as a stochastic process. We find that for finely resolved data the
transitions are effectively Markovian, but for larger decimation time lags, due
to topological mode degeneracy, non-Markovian behavior emerges, in agreement
with previous experimental studies.
