Spinning fluid vortices on a curved neck of water are pushed around by the slope of the curvature itself rather than just the curve.
April 29, 2026
Original Paper
Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Drift Dynamics
arXiv · 2604.25682
The Takeaway
Fluid dynamics on a catenoid surface reveal a weird transport mechanism that does not exist on flat ground. Pairs of vortices orbiting each other will drift across the surface based on the gradient of the Gaussian curvature. This means the change in how the surface bends acts as a physical force that steers the fluid. This discovery changes how scientists model weather patterns on non-spherical planets or fluids flowing through complex biological membranes. It proves that the geometry of a container can be used as a remote control for the movement of the liquid inside.
From the abstract
Vortices in fluids and superfluids underpin phenomena ranging from Bose--Einstein condensates and superfluid films to neutron stars and hydrodynamic micro-rotors, where geometry can strongly influence their motion. Curvature can induce vortex motion with no planar analogue. We study Hamiltonian vortex motion on a catenoid, a minimal surface of variable negative curvature, and derive explicit equations of motion, conserved quantities, and reductions for co-rotating vortex pairs. For two identical