An Application of Kolmogorov Complexity and Its Spectrum to Positive Surges

Abstract

A positive surge is associated with a sudden change in flow that increases the water depth and modifies flow structure in a channel. Positive surges are frequently observed in artificial channels, rivers, and estuaries. This paper presents the application of Kolmogorov complexity and its spectrum to the velocity data collected during the laboratory investigation of a positive surge. Two types of surges were considered: a undular surge and a breaking surge. For both surges, the Kolmogorov complexity (KC) and Kolmogorov complexity spectrum (KCS) were calculated during the unsteady flow (US) associated with the passage of the surge as well as in the preceding steady-state (SS) flow condition. The results show that, while in SS, the vertical distribution of KC for Vx is dominated by the distance from the bed, with KC being the largest at the bed and the lowest at the free surface; in US only the passage of the undular surge was able to drastically modify such vertical distribution of KC resulting in a lower and constant randomness throughout the water depth. The analysis of KCS revealed that Vy values were peaking at about zero, while the distribution of Vx values was related both to the elevation from the bed and to the surge type. A comparative analysis of KC and normal Reynold stresses revealed that these metrics provided different information about the changes observed in the flow as it moves from a steady-state to an unsteady-state due to the surge passage. Ultimately, this preliminary application of Kolmogorov complexity measures to a positive surge provides some novel findings about such intricate hydrodynamics processes.

Keywords

• environmental hydraulics
• positive surge
• undular surge
• breaking surge
• information measures
• Kolmogorov complexity