Lower Bounds on Scalar Dissipation in Bounded Rectilinear Flows

Lower bounds on the scalar dissipation rate in rectilinear flows are found for three sets of constraints. The bounding dissipation rates provide upper bound estimates of the scalar concentration variance. One of the lower bounds on the dissipation rate is close to the dissipation rate assessed from detailed numerical simulation. This proximity enables a simplified model of concentration variance. For a pulse input of solute, the predictions of concentration variance by the simplified model are in agreement with the results of detailed simulation. The large-time bimodality of the concentration variance and its rate of decay observed in the detailed numerical simulations is predicted by the simplified model.