Vortex dynamics on a Möbius strip

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