Elongation of material lines and vortices by Euler flows on two-dimensional Riemannian manifolds
Abstract
Abstract We study the influence of the differential geometry of the flow domain on the motion of fluids on two-dimensional Riemannian manifolds, particularly on the elongation of material lines and vortices. We derive a formula for the second order time derivative of the square of the distance between close fluid particles and show that a curvature term appears. The elongation of a material line is accelerated by negative curvature. The use of this expression extends Haller’s definition of hyperbolic domains to flows on curved surfaces. The need to consider curvature effects is illustrated by three examples. The example of a curved two-dimensional torus implies that the filamentation of vortices can be triggered by negative curvature.
Fields of Study & Subjects
Micro and Nano Robotics
Geometric Analysis and Curvature Flows
Fluid dynamics and aerodynamics studies
Publication details
- Journal / source
- Fluid Dynamics Research
- Publisher
- IOP Publishing
- Volume
- 58
- Issue
- 1
- Pages
- 015501–015501
- Publication date
- 1 February 2026
- Language
- EN