Vortex dynamics on a Mobius strip

We consider the dynamics of a two-dimensional incompressible perfect fluid on a Mobius strip embedded in R-3. The vorticity-stream function formulation of the Euler equations is derived from an exterior-calculus form of the momentum equation. The non-orientability of the Mobius strip and the distinction between forms and pseudo-forms this introduces lead to unusual properties: a boundary condition is provided by the conservation of circulation along the single boundary of the strip, and there is no integral conservation for the vorticity density or for any odd function thereof. A finite-difference numerical implementation is used to illustrate the Mobius-strip realisation of familiar phenomena: translation of vortices along boundaries, shear instability and decaying turbulence.

Automated summary

This study investigates the dynamics of a two-dimensional incompressible perfect fluid on a Mobius strip embedded in R-3, deriving the vorticity-stream function formulation of the Euler equations. The non-orientability of the Mobius strip leads to unique properties and challenges, with a focus on circulation conservation along the strip's single boundary and the absence of integral conservation for vorticity density or odd functions. A finite-difference numerical implementation illustrates phenomena like vortex translation, shear instability, and decaying turbulence on the Mobius strip.