Stochastic analysis and modeling of velocity observations in turbulent flows

Highly turbulent water flows, often encountered near human constructions like bridge piers, spillways, and weirs, display intricate dynamics characterized by the formation of eddies and vortices. These formations, varying in sizes and lifespans, significantly influence the distribution of fluid velocities within the flow. Subsequently, the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels. For this reason, to meticulously study these dynamics, more often than not, physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures. Despite the effectiveness of physical modeling, various monitoring challenges arise, including flow disruption, the necessity for concurrent gauging at multiple locations, and the duration of measurements. Addressing these challenges, image velocimetry emerges as an ideal method in fluid mechanics, particularly for studying turbulent flows. To account for measurement duration, a probabilistic approach utilizing a probability density function (PDF) is suggested to mitigate uncertainty in estimated average and maximum values. However, it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses. In response, this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications. This integration enables an approach based on the probability of failure, facilitating a more comprehensive analysis of turbulent flows. Such an approach is essential for estimating both short- and long-term stresses on hydraulic constructions under assessment.