Fluid Dynamics on a Möbius Strip

We can arrange an odd number of convection cells into a continuous velocity field on a Möbius strip. This construction does not correspond to a known physical setting but provides a test case to illustrate and test methods developed for fluid analysis on Riemannian manifolds. The blue and red curves are attracting and repelling curves, respectively, which give a skeleton of the fluid flow in this first instance of Lagrangian coherent structures (LCS) for a non-orientable manifold.
▶️ Learn more at the video Lagrangian Coherent Structures- Introduction
• Lagrangian Coherent St...
► Dr. Shane Ross is a Professor at Virginia Tech. He has a Ph.D. from Caltech (California Institute of Technology) and worked at NASA/JPL and Boeing.
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► Links to related journal article PDFs
The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds, Chaos 20, 017505 (2010).
shaneross.com/p...
Chaotic advection in the restricted four-vortex problem on a sphere, Physica D: Nonlinear Phenomena 223(1), 36-53 (2006).
shaneross.com/p...
Finite-time Lyapunov exponents in the instantaneous limit and material transport, Nonlinear Dynamics, 100:3825-3852 (2020).
shaneross.com/p...
Detection and characterization of transport barriers in complex flows via ridge extraction of the finite time Lyapunov exponent field, International Journal for Numerical Methods in Engineering 86, 1163-1174 (2011).
shaneross.com/p...
Pollution transport patterns obtained through generalized Lagrangian coherent structures, Atmosphere 11, 168 (2020).
shaneross.com/p...
► Related Courses and Series Playlists by Dr. Ross
📚Lagrangian Coherent Structures
is.gd/LCSvideos
📚3-Body Problem Orbital Dynamics Course
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📚Space Manifolds
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📚Space Vehicle Dynamics
is.gd/SpaceVeh...
📚Lagrangian and 3D Rigid Body Dynamics
is.gd/Analytic...
📚Nonlinear Dynamics and Chaos
is.gd/Nonlinea...
📚Hamiltonian Dynamics
is.gd/Advanced...
📚Center Manifolds, Normal Forms, and Bifurcations
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[@JAYMOAP]

"In our recent work, we introduced the optical analogue Skyrmionic Hopfion [14] as a particle-like field configuration in three dimensions. This structure can be considered both, a Hopfion and an optical, three-dimensional (3d) Skyrmion in free-space light. The polarization pattern of this field constructs the projection of the Hopf-fibration in real 3d space. In this structure, each polarization state on the Poincaré sphere exists along a filament that forms a circle, which is threading through to all other circular filaments of constant polarization. Along such a filament, the phase varies continuously by 2𝜋
, which is why the configuration becomes a 3d Skyrmion. The object is threaded by polarization singularities in the form of C-Lines (purely circular states of polarization in a field of elliptical polarization), that can be considered as its skeleton." 👌