National Oceanic and
Atmospheric Administration
United States Department of Commerce


FY 1985

The exchange of water in fjords: The efflux/reflux theory of advective reaches separated by mixing zones

Cokelet, E.D., and R.J. Stewart

J. Geophys. Res., 90(C4), 7287–7306, doi: 10.1029/JC090iC04p07287 (1985)

Many fjords consist of deep, stratified reaches separated by shallower sills above which most of the mixing between water masses occurs. On a long time scale, each reach can be modeled as a steady, two-layer advective flow. These flows intermingle in turbulent mixing zones, where the flow from any incoming layer can be split into two parts: an efflux fraction, which continues on into the next reach, and a reflux fraction, which mixes vertically and recirculates into its original reach. Using conservation of mass, we define these fractions and express them in terms of the salinities observed in the reaches. The processes of the complex mixing zones need not be considered in detail. These ideas are applicable to complicated branched fjords and linked sequences of reaches. Where more than two reaches meet at a multiple junction the conservation of two tracers (usually fresh water and salt) is insufficient to determine completely the efflux/reflux fractions. We propose an entropy maximization technique to resolve the uncertainty. Long-term pollutant concentrations relate directly to the circulation via the new efflux/reflux formulation. The method demonstrates that refluxing leads to conservative pollutants being broadcast throughout the fjord system with magnified concentrations. A new quantity, the mean tracer age, provides a relevant time scale that includes the effects of recirculation and to which the rates of non-conservative processes should be compared. Conservative pollutants may be retained for a surprisingly long time in a refluxing system.

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