Hans Burchard, Leibniz Institute of Baltic Sea Research Warnemünde, Germany


Physical and numerical water mass transformations in numerical models of estuarine systems


First, the Knudsen theorem for estuarine exchange flow, based on mass conservation of water and salt, and its generalization with resolution in salinity coordinates, the Total Exchange Flow (TEF) analysis framework, are reviewed. The former had been developed, and applied to quantify exchange flow between the North Sea and the Baltic Sea, more than a century ago. Using the Knudsen theorem and the TEF analysis framework, validated multi-decadal (years 1949–2013) model simulations are analyzed in terms of exchange flow through straits of the Western Baltic Sea. The model-based long-term Knudsen and TEF analyses of exchange flow in the Western Baltic Sea reproduces the Major Baltic Inflows (MBIs) that have occurred since the 1950s.

Secondly, the Knudsen theorem and the TEF analysis framework are used to quantify estuarine salt mixing, defined as the decay of salinity variance due to turbulent mixing. In addition to the advective fluxes, diffusive fluxes across the boundary are also considered now. These new Knudsen and TEF relations for mixing are derived by applying Gauss’s theorem to the salinity square and salinity variance equations. As a result of the analysis, four different Knudsen relations for the mixing in estuaries are derived, the most simple of which estimates the estuarine mixing as the product of inflow salinity, outflow salinity, and time-averaged river runoff. The four mixing estimates are systematically assessed by means of a number of idealized estuarine test cases. For periodic tidal flow, the simplest estimate still predicts the effective mixing, composed of physically-induced (due to the turbulence closure model) and numerically-induced (due to truncation errors of the salt advection scheme) mixing, within an error of about 10%.

Finally, the above mixing analysis is extended towards isohaline coordinates to quantify the salt mixing per salinity class as a measure for the water mass transformation rate. As a result, the long-term averaged mixing per salinity class is twice the respective salinity times the freshwater run-off. For numerical models of estuarine systems, this mixing per salinity class is the effective mixing  (physical plus numerical). 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 the inflow and outflow salinities (universality), (ii) it is exactly derived from conservation laws (accuracy) and (iii) it calculates mixing per salinity class (locality).


Tuesday October 1, 11:15


Rossbysalen C609, Arrhenius laboratory, Svante Arrhenius väg 16C, 6th floor