Asymptotic higher linking in volume preserving flows

The topology of orbits in volume-preserving flows is of special interest in the area of fluid dynamics and plasma physics. The well-known helicity invariant measures an asymptotic average linking number of orbits of the flow and gives an estimate for the $L^2$--energy of the field. Invariants of flows obtained from higher linking numbers were only derived under special assumptions on the domain of the field or rely on the special features of the vector field. In this talk, I will present preliminary results on an irregular asymptotic invariant obtained from the triple linking number.