Two outfalls in an estuary: Cooperative pollution minimization

Two outfalls, each with given tidally averaged discharge rates, are discharging into the same narrow (rapidly mixed) estuary. The lowest achievable concentration peak (in position and time) for the principal contaminant species is attained with an ‘all or nothing’ discharging policy. The discharge rate is either ‘all’ that is allowed by concentration peak or is nothing. The ‘nothing’ regime corresponds to the water from the outfall with the relatively small discharge load, which would otherwise have carried the principal contaminant species to the other outfall with the least decay. Constructive (exact) algorithms are presented for the ‘all or nothing’ partition and for the cooperative discharge rates at the two outfalls.