Variational construction of tubular and toroidal streamsurfaces for flow visualization

Li, Mingwu1; Kaszas, Balint2; Haller, George2

2024-03-13

10.1098/rspa.2023.0951

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES   影响因子和分区

1364-5021

1471-2946

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor-Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh-Benard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh-Benard convection.

first integral coherent structures finite-element methods

SCI ; EI

英语

第一 ; 通讯

Science & Technology - Other Topics

Multidisciplinary Sciences

WOS:001183151100007

ROYAL SOC

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China
2.Swiss Fed Inst Technol, Inst Mech Syst, Leonhard Str 21, CH-8092 Zurich, Switzerland

Li, Mingwu,Kaszas, Balint,Haller, George. Variational construction of tubular and toroidal streamsurfaces for flow visualization[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,2024,480(2285).

Li, Mingwu,Kaszas, Balint,&Haller, George.(2024).Variational construction of tubular and toroidal streamsurfaces for flow visualization.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,480(2285).

Li, Mingwu,et al."Variational construction of tubular and toroidal streamsurfaces for flow visualization".PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 480.2285(2024).