Diahaline mixing at the estuary - river plume continuum

In classical estuaries, salty ocean water is mixed with riverine freshwater such that brackish water is produced. To provide salt water for mixing in a long-term averaged estuarine state, ocean water needs to enter the estuary across a fixed estuarine transect at higher salinity classes (at a rate of Q_in) while brackish water is ejected seawards at lower salinity classes (at a rate of Q_out), establishing the estuarine exchange flow. This transect may be located anywhere in the estuary - river plume continuum. If no mixing takes place inside the estuary, riverine freshwater will leave the estuary across the transect (at zero salinity) and no salt water can enter, such that Q_in=0. Thus, when formulated in salinity coordinates, estuarine mixing and exchange flow are directly related to each other. With this, Q_in is a suitable measure for the exchange flow. This relation is approximately represented by the Knudsen mixing relation M=s_ins_outQ_r=(s_in-s_out)s_inQ_in, where M is the mixing (salinity variance decay), s_in and s_out are the characteristic salinities of the inflow and the outflow, respectively, and Q_r is the river runoff. A recently published relation between exchange flow and mixing relies on the distribution of diahaline mixing: Q_in=-1/2 dm_est(s_div)/dS, where m_est(s) is the diahaline mixing per salinity class across the part of the isohaline with salinity s which is situated inside the estuarine transect and s_div is the dividing salinity between inflow and outflow across the transect with s_in>s_div>s_out. In this presentation, a method is presented how to directly calculate  m_est(s_div) from s_in, s_div, s_out and Q_r. A respective relation for the part of the isohaline outside the transect is derived as well. The relation between the three estuarine mixing quantifications is presented and their usefulness for the estuary - river plume continuum is discussed.