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 bou
nds 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 co
ncentration variance by the simplified model are in agreement with the resu
lts of detailed simulation. The large-time bimodality of the concentration
variance and its rate of decay observed in the detailed numerical simulatio
ns is predicted by the simplified model.