Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains
76
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs) [Serra & Haller, 2016], material barriers to diffusive transport [Haller et al., 2018, Haller et al., 2019], and constrained diffusion barriers [Haller et al., 2019]. The method builds on ideas developed previously in [Karrasch et al., 2015], but our implementation alleviates a number of shortcomings and allows for the fully automated detection of such vortices on unprecedentedly challenging real-world flow problems, for which specific human interference is absolutely infeasible. Challenges include very large domains and/or parameter spaces. We demonstrate the efficacy of our method in dealing with such challenges on two test cases: first, a parameter study of a turbulent flow, and second, computing material barriers to diffusive transport in the global ocean.
rate research
Read More
We have performed Coherent-vorticity Preserving Large-Eddy simulations of a trefoil knot-shaped vortex, inspired by the experiments of Kleckner and Irvine. The flow parameter space is extended in the present study, including variations of the circulation Reynolds numbers in the range Re = 2000 - 200000, where Re = 20000 is the value used in the experiments. The vortex line corresponding to the trefoil knot is defined using a parametric equation and the Biot-Savart law is employed to initialize the velocity field. The CvP LES computation displays a good qualitative match with the experiment. In particular, the vortex entanglement process is accurately represented as well as the subsequent separation of the main vortex in two distinct structures - a small and a large vortex - with different self-advection speeds that have been quantified. The small vortex propagates faster than the large oscillatory vortex which carries an important amount of vorticity. The advection velocity of the vortex before bursting is found to be independent of the Reynolds number. The low Reynolds number computation leads to a decrease of the separated vortices velocity after bursting, compared to the higher Reynolds computations. The computation of energy spectra emphasizes intense energy transfers from large to small scales during the bursting process. The evolution of volume-averaged enstrophy shows that the bursting leads to the creation of small scales that are sustained a long time in the flow, when a sufficiently large Reynolds number is considered (Re>20000). The low Reynolds number case Re = 2000 hinders the generation of small scales during the bursting process and yields essentially laminar dynamics. The onset of background turbulence due to the entanglement process can be observed at Re = 200000
We develop a framework to study the role of variability in transport across a streamline of a reference flow. Two complementary schemes are presented: a graphical approach for individual cases, and an analytical approach for general properties. The spatially nonlinear interaction of dynamic variability and the reference flow results in flux variability. The characteristic time-scale of the dynamic variability and the length-scale of the flux variability in a unit of flight-time govern the spatio-temporal interaction that leads to transport. The non-dimensional ratio of the two characteristic scales is shown to be a a critical parameter. The pseudo-lobe sequence along the reference streamline describes spatial coherency and temporal evolution of transport. For finite-time transport from an initial time up to the present, the characteristic length-scale of the flux variability regulates the width of the pseudo-lobes. The phase speed of pseudo-lobe propagation averages the reference flow and the flux variability. In contrast, for definite transport over a fixed time interval and spatial segment, the characteristic time-scale of the dynamic variability regulates the width of the pseudo-lobes. Generation of the pseudo-lobe sequence appears to be synchronous with the dynamic variability, although it propagates with the reference flow. In either case, the critical characteristic ratio is found to be one, corresponding to a resonance of the flux variability with the reference flow. Using a kinematic model, we demonstrate the framework for two types of transport in a blocked flow of the mid-latitude atmosphere: across the meandering jet axis and between the jet and recirculating cell.
Advances in time-resolved Particle Tracking Velocimetry (4D-PTV) techniques have been consistently revealed more accurate Lagrangian particle motions. A novel track initialisation technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbour trajectories, is proposed. The proposed Lagrangian Coherent Track Initialisation (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine the boundaries (i.e., ridges) of Lagrangian Coherent Structures (LCS) among neighbour trajectories by using FTLE to distinguish clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from 3D Direct Numerical Simulation (DNS). The dataset is available to the public. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behaviour in finding true tracks compared to the recent initialisation algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks are also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian Particle Tracking challenge for a flow with high particle densities. Finally, the LCTI behaviour was assessed in a real jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high particle concentrations.
Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction that has been designed specifically for purely advective dynamics. The construction is based on a dynamic Laplacian operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly.
We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine-Hugoniot conditions in arbitrary spatial configuration of the tubes, and compute several examples of particular solutions. The theory is derived from a variational treatment of Cosserat rod theory extended to incorporate expandable walls and moving flow inside the tube. The results presented here are useful for biological flows and industrial applications involving high speed motion of gas in flexible tubes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
