Mass and salt transfers and halocline depths in an estuary

The paper considers fluxes of brackish and ocean water out of and into an estuary as well as the depth of the halocline in the estuary. The discussion ignores the details of the mass distribution and circulations in the main body of the estuary (except for the halocline depth) and concentrates on determining the flow conditions and interface depths in the vicinity of the mouth. The flow there is considered to be frictionless and the pressure hydrostatic, and the first part of the analysis, which assumes strong mixing (and, therefore, a deep halocline) in the estuary, yields the same results as those of Stommel and Farmer for their “overmixed” state. Phenomena in this state are determined by a non-dimensional number Q proportional to the fresh water influx q_f. On the other hand, the problem can also be solved when the mixing is zero. The two extreme cases suggest a dependence on a mixing number M for arbitrary mixing. This permits a complete solution for the ocean water flux, brackish water flux, depth of the interface at the mouth, salinity of the brackish water, depth of the halocline in the main body of the estuary and height above sea level of the free surface in the estuary, all as functions of Q_f and M. An interesting feature of all solutions is the main halocline depth which always becomes large for both weak and strong fresh water fluxes and therefore has a minimum at a value q_fm which varies with M. This behavior has been observed in Alberni Inlet in British Columbia and in a laboratory experiment by Welander. Comparison of theory with the Baltic Sea leads to some numerical results and speculations.