A Universal Law of Estuarine Mixing

A universal law of estuarine mixing is derived here, combining the approaches of salinity coordinates, Knudsen relations, total exchange flow, mixing definition as salinity variance loss, and the mixing-exchange flow relation. As a result, the long-term average mixing within an estuarine volume bounded by the isohaline of salinity S amounts to M(S) = S(2)Q(r), where Q(r) is the average river runoff into the estuary. Consequently, the mixing per salinity class is m(S) = partial differential M-S(S) = 2SQ(r), which can also be expressed as the product of the isohaline volume and the mixing averaged over the isohaline. The major differences between the new mixing law and the recently developed mixing relation based on the Knudsen relations are threefold: (i) it does not depend on internal dynamics of the estuary determining inflow and outflow salinities (universality), (ii) it is exactly derived from conservation laws (accuracy), and (iii) it calculates mixing per salinity class (locality). The universal mixing law is demonstrated by means of analytical stationary and one-dimensional and two-dimensional numerical test cases. Some possible consequences for the salinity distribution in real estuaries are briefly discussed. Since the mixing per salinity class only depends on the river runoff and the chosen salinity, and not on local processes at the isohaline, low-mixing estuaries must have large isohaline volumes and vice versa.