Mixing Pathways in Simple Box Models

Tracer variance budgets can be used to estimate bulk mixing in a control volume. For example, simple, analytical, bulk formulations of salt mixing, defined here as the destruction of salinity variance, can be found for estuaries with a riverine source of freshwater and a two-layer exchange flow at the mouth using salinity as a representative tracer. For a steady case, the bulk salt mixing M can be calculated as M=Q(R)S(out)(2)+Qin(S-out-S-in)(2), where S-in and S-out are the representative salinities in the estuarine exchange flow, and Q(R) and Q(in) are the river and landward volume fluxes, respectively. The bulk salt mixing M can be considered as the sum of mixing pathways, where each pathway has a mixing of Q(delta S)(2), where Q is the volume transport and delta S is the salinity difference across the pathway. For the estuary case, one mixing path is associated with the river inflow, and the other is associated with the inflow of salty, oceanic water. This concept of linking mixing to input-output pathways is extended, in simple box models, from estuaries to scenarios with multiple inputs/outputs, as might be found in a complex estuarine/fjord network, in a region on a continental shelf, or any other control volume with multiple exchanges. This approach allows for the estimation of the relative contributions of each input-output pathway to the total mixing within a control volume.