Estuarine Exchange Flow Is Related to Mixing through the Salinity Variance Budget

The relationship between net mixing and the estuarine exchange flow may be quantified using a salinity variance budget. Here mixing'' is defined as the rate of destruction of volume-integrated salinity variance, and the exchange flow is quantified using the total exchange flow. These concepts are explored using an idealized 3D model estuary. It is shown that in steady state (e.g., averaging over the spring-neap cycle) the volume-integrated mixing is approximately given by Mixing congruent to S(in)S(out)Q(r), where S-in and S-out are the representative salinities of in- and outflowing layers at the mouth and Q(r) is the river volume flux. This relationship provides an extension of the familiar Knudsen relation, in which the exchange flow is diagnosed based on knowledge of these same three quantities, quantitatively linking mixing to the exchange flow.