Variational construction of tubular and toroidal streamsurfaces for flow visualization

Author:

Li Mingwu1ORCID,Kaszás Bálint2ORCID,Haller George2ORCID

Affiliation:

1. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055,People’s Republic of China

2. Institute for Mechanical Systems, ETH Zürich Leonhardstrasse 21, Zürich 8092, Switzerland

Abstract

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–Bénard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh–Bénard convection.

Publisher

The Royal Society

Reference34 articles.

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2. Illustrative Stream Surfaces

3. Schulze M Esturo JM Günther T Rössl C Seidel H-P Weinkauf T Theisel H. 2014 Sets of globally optimal stream surfaces for flow visualization. Computer Graphics Forum 33 1–10. (doi:10.1111/cgf.12356)

4. Hultquist JP. 1992 Constructing stream surfaces in steady 3D vector fields. In Proc. Visualization ’92 Boston MA 19–23 October pp. 171–178. IEEE.

5. On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

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