Laminar mixing of fluids and scalars: a unified Hamiltonian approach

Scalar transport fundamentally is the transport of ``parcels'' of a given scalar quantity by the total advective-diffusive scalar flux in an analogous manner as fluid motion is the transport of fluid parcels by the flow. This fundamental analogy between scalar transport and fluid motion admits application of Hamiltonian methods well-known from laminar mixing studies to laminar scalar transport. Key to these methods is description of fluid advection -- and the mixing properties -- in terms of the geometry of the fluid trajectories (``flow topology''). These Hamiltonian methods facilitate investigation of the geometry of the scalar trajectories (``scalar topology'') -- and thus the scalar transport -- in an entirely analogous manner. The unified Hamiltonian approach and its potential for investigation of laminar scalar transport is demonstrated by way of example.