2016/02/17 by Daniel Lester, Marco Dentz, Lester, Daniel R. +5 · 2 citations
Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Lattice Boltzmann Simulation Studies #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.1602.05273
openalex publication_date 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as finite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincaré-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical and non-helical, compressible and incompressible flows, and find random flows exhibit remarkably simple (Gaussian) deformation structure, and so are fully characterised in terms of a small number of parameters. As such this technique provides the basis for the development of stochastic models of fluid deformation in random flows which adhere to the kinematic constraints inherent to various flow classes.