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The complexity or randomness of the laminar-turbulent transition process of an inlet boundary layer in a circular pipe was analyzed by use of Kolmogorov complexity which is a very important measure of the randomness of various events. In the inlet region of the circular pipe, a jet that triggered a turbulent patch in the flow was periodically injected radially, and then propagated downstream periodically. Periodic velocity data which satisfies the phase constancy obtained from a hot-wire anemometer were compressed using a compression program running on a Windows PC. From the compressed data, the approximated Kolmogorov complexity, named AK, and normalized compression distance NCD were obtained. Although the distribution of AK of irregularly fluctuating velocity in the flow showed a slight discrepancy from the profile of fluctuating velocity intensity and intermittency factor, they exhibited qualitative consistency. Therefore, the objective judgment of the laminar-turbulent transition process based on the approximated Kolmogorov complexity mostly supports the conventional judgment. In conclusion, our study established the validity and usefulness of Kolmogorov complexity or algorithmic complexity to describe objectively the laminar-turbulent transition process in the mixing layer, flat plate boundary layer and pipe flow. With the aid of the AK we can distinguish the complexity within the turbulent region; on the other hand, the intermittency factor cannot.

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Randomness representation in turbulent flows with Kolmogorov complexity (In laminar-turbulent transition due to periodic injection in an inlet boundary layer in a circular pipe)