Transport in 3D volume-preserving flows (Q1332263)

The paper is concerned with the volume-preserving flow generated by a steady \(C^ 1\) divergence free vector field \(\mathbf u\) in a 3D region \(\Omega\). The notion of a surface of locally minimal flux of \(\mathbf u\) is introduced. Two examples are discussed, illustrating that the skeleton formed by the equilibrium points, selected hyperbolic periodic orbits and cantori and (some) connecting orbits provides a complex of surfaces of locally minimal flux. The two examples are `spheromaks' (spherical vortices) and eccentric Taylor-Couette flows.