Stretching and folding analysis of fluid based on covariance method

• Published in: Physica scripta Vol. 99; no. 8; pp. 85611 - 85621
• Main Authors: Wei, Zeming, Wang, Boxuan
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.08.2024
• Subjects: nonlinear deformation; stretching and folding; transport and mixing
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ad63e2

Abstract Fluid in a turbulent state will be continuously stretched and folded, and the boundaries of fluid elements will grow exponentially, leading to an intense mixing process between different regions. However, most studies focus on the fluid’s stretching process, and the definition of folding still needs to be clarified. In this paper, the covariance method is extended to study the nonlinear deformation of fluid. First, particle sets are used to characterize the fluid elements, and the evolution of particle sets could reflect the deformation process of fluid. Then, the stretching and folding degrees of fluid are defined based on the statistical parameters of the particle sets. Finally, the extended covariance method is applied to the double gyre and the flow around the square cylinder, and the results show that the stretching process dominates the early stage of fluid deformation, and the fluid in high stretching regions has a higher probability of folding. Importantly, the nonlinear stretching regions with high non-affine deformation-low folding properties are identified, and the spurious folding caused by nonlinear stretching is eliminated. In summary, the extended covariance method shows great potential in the nonlinear deformation analysis of fluid, contributing to a deeper understanding of transport and mixing.