Joint Seminar: Estuarine mixing and exchange flow in an isohaline framework

For estuaries, which are transitions zones between rivers and the ocean and where the density is dominated by salinity, the isohaline framework offers new perspectives of analysing estuarine mixing and exchange flow.

Mixing. It has been recently shown (Burchard, 2020) that the long-term averaged mixing (reduction rate of salinity variance) in an estuarine volume bounded by a moving isohaline of salinity S amounts to M(S)=S2Qr , where Qr is the river discharge. With this universal law of estuarine mixing, the mixing per salinity class amounts to m(S)=dM(S)/dS=2SQr. In a numerical model, this mixing is composed of parameterised (physical) mixing and numerical mixing due to the truncation error of advection schemes (Klingbeil et al., 2014). To quantify this in an isohaline framework, the local mixing rates are binned into salinity classes for each water column giving the local mixing per salinity class, showing for each salinity class the horizontal composition of m. Long-term averaging and integration of total mixing (sum of physical and numerical mixing) over the isohaline surface gives the universal law.

Exchange flow. The diahaline velocity can be calculated by means of binning local layer thicknesses into salinity classes, taking the isohaline slope into consideration. Integration of over the entire isohaline surface and long-term averaging gives the diahaline volume transport which should be equal to Qr. The local composition shows a diahaline exchange flow with some regions of up-estuary (towards lower salinity) volume transport and more pronounced regions of down-estuary (towards higher salinity) volume transport. Integrating separately over all up-estuary and down-estuary contributions gives the diahaline exchange flow.

Connection between mixing and exchange flow. Locally, mixing per salinity class and the diahaline velocity are connected through a fundamental relation: The diahaline velocity equals minus half of the S-gradient of the local mixing per salinity class. This relation is shown for a realistic estuarine application to the Baltic Sea. For large-scale ocean applications, comparable diapycnal concepts have been developed Ferrari et al. (2016).



Burchard, H., A universal law of estuarine mixing. J. Phys. Oceanogr., 50, 81-93, 2020.

Ferrari, R., Mashayek, A., McDougall, T. J., Nikurashin, M., & Campin, J. M. Turning ocean mixing upside down. J. Phys. Oceanogr., 46, 2239-2261, 2016.

Klingbeil, K., M. Mohammadi-Aragh, U. Gräwe, and H. Burchard, Quantification of spurious dissipation and mixing – Discrete Variance Decay in a Finite-Volume framework, Ocean Modelling, 81, 49-64, 2014.

Li, X., M. Lorenz, K. Klingbeil, E. Chrysagi, U. Gräwe, J. Wu, H. Burchard, Diahaline mixing and exchange flow in a large multi-outlet estuary with islands, J. Phys. Oceanogr., 52, 2111-2127, 2022.




13:30–14:30 Uhr


Bundesstr. 53, room 022/023
Seminar Room 022/023, Ground Floor, Bundesstrasse 53, 20146 Hamburg, Hamburg


Hans Burchard, Leibniz Institute for Baltic Sea Research


Bo Liu

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