Topology of advective-diffusive scalar transport in laminar flows

The present study proposes a unified Lagrangian transport template for topological description of advective fluid transport and advective-diffusive scalar transport in laminar flows. The key to this unified description is the expression of scalar transport as purely advective transport by the total scalar flux. This admits generalization of the concept of transport topologies known from laminar mixing studies to scalar transport. The study is restricted to two-dimensional systems and the fluid and scalar transport topologies, as a consequence, prove to be Hamiltonian. The unified Lagrangian transport template is demonstrated and investigated for a heat-transfer problem with nonadiabatic boundaries, representing generic scalar transport with permeable boundaries. The fluid and thermal transport topologies under steady conditions both accommodate islands (constituting isolated flow and thermal regions) that undergo Hamiltonian disintegration into chaotic seas upon introducing time periodicity. The thermal transport topology invariably comprises transport conduits that connect the nonadiabatic boundaries and facilitate wall-wall and wall-fluid heat transfer. For steady conditions these transport conduits are regular; for time-periodic conditions these conduits may, depending on degree of diffusion, be regular or chaotic. Regular conduits connect nonadiabatic walls only with specific flow regions; chaotic heat conduits establish connection (and thus heat exchange) of the nonadiabatic walls with the entire flow domain.