Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

Investigations of the definition and randomness of turbulence were reviewed. The Kolmogorov complexity measure of randomness was then introduced. Numerical and graphic data in the mixing layer formed downstream of a two-dimensional nozzle exit were compressed with the aid of a compression program. Approximated Kolmogorov complexity, AK, and normalized compression distance, NCD, were obtained. The AK indicated the regularity of the laminar flow and the randomness of the turbulent flow quantitatively. The NCD of the numerical value varied with data length. Between the same data, it approached zero, yet, between different data, it approached unity as the data length increased. The NCD of the numerical value in the natural transition process in the mixing layer increased monotonically downstream. Thus, the NCD appears to be the measure of the transition process. In the natural transition process in the mixing layer, the AK of the numerical value and the NCD of the graphic data did not change monotonously in the downstream direction. They therefore contain some uncertainty for measurement of the transition process.