  Numerical and experimental studies of transitional pipe flow have shown the
prevalence of coherent flow structures that are dominated by downstream
vortices. They attract special attention because they contribute predominantly
to the increase of the Reynolds stresses in turbulent flow. In the present
study we introduce a convenient detector for these coherent states, calculate
the fraction of time the structures appear in the flow, and present a Markov
model for the transition between the structures. The fraction of states that
show vortical structures exceeds 24% for a Reynolds number of about Re=2200,
and it decreases to about 20% for Re=2500. The Markov model for the transition
between these states is in good agreement with the observed fraction of states,
and in reasonable agreement with the prediction for their persistence. It
provides insight into dominant qualitative changes of the flow when increasing
the Reynolds number.
