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arXiv · 2604.25682

Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Curvature-Induced Drift

Gaurang Mangesh Joshi·Rickmoy Samanta
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Abstract

Vortices in fluids and superfluids are fundamental to phenomena ranging from Bose-Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where background geometry often plays an important role. Curvature can induce vortex motion distinct from planar domains. We study Hamiltonian vortex motion on a catenoid, a minimal surface of variable negative curvature, and derive explicit equations of motion and conserved quantities for co-rotating vortex pairs. For two identical vortices we find an exact analytic solution in which the pair rotates rigidly at fixed latitude, with angular velocity $\Omega=(\Gamma/16\pi)\,K'(V)/\sqrt{-K(V)}$, where $K(V)$ is the Gaussian curvature. Thus the motion is governed by the curvature gradient rather than the curvature itself. This state is linearly unstable, with growth rate $\lambda=\sqrt{3}|\Omega|$, in agreement with numerical simulations. For generic co-rotating pairs, conservation of the Hamiltonian and rotational momentum reduces the nonlinear dynamics to a single quadrature, yielding bounded relative oscillations together with a secular azimuthal drift. Simulations of the full equations confirm this and reveal the same curvature-induced azimuthal drift in a localized many-vortex cluster, motivating a broader theory of collective vortex drift on curved surfaces.

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math-phcond-mat.quant-gasmath.MPnlin.SIphysics.flu-dyn

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Gaurang Mangesh Joshi, Rickmoy Samanta. 2026-04-28. Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Curvature-Induced Drift. https://doi.org/10.1515/tp-2026-0057

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