Mixing Estimates for Estuaries

Burchard, Hans; Lange, Xaver; Klingbeil, Knut; MacCready, Parker

doi:10.1175/jpo-d-18-0147.1

Cited by 23 publications

(56 citation statements)

References 26 publications

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“…To demonstrate the different convergence behaviours of the sign method and the dividing salinity method, we take the analytical example from Burchard et al (2018b). It describes a well-mixed tidal flow with oscillating salinity as it occurs e.g.…”

Section: Convergence Analysis For An Analytical Classical Exchange Flowmentioning

confidence: 99%

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Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

Lorenz¹,

Klingbeil²,

MacCready³

et al. 2019

Preprint

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Abstract. For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange flow (TEF) which uses salinity coordinates to calculate these bulk quantities allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values for an increasing number of salinity classes. In the present study, this problem is investigated and the method of dividing salinities, described by MacCready et al. (2018), is mathematically introduced. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.

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Section: Convergence Analysis For An Analytical Classical Exchange Flowmentioning

confidence: 99%

“…The mixing relations of MacCready et al (2018) and Burchard et al (2018b) require only one value each for the inflow properties and outflow properties, respectively. These can be obtained from a multi-layer transect by applying weighted averages, i.e.…”

mentioning

confidence: 99%

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

Lorenz¹,

Klingbeil²,

MacCready³

et al. 2019

Preprint

Self Cite

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show abstract

“…The same concept of isohaline volumes [infinitesimal volume dV included in an infinitesimal salinity interval dS, see Eq. (25) of the present manuscript] and their change due to advective and diffusive diahaline transports has been used by MacCready et al (2002) to explain the long-term isohaline structure of tidal estuaries. Hetland (2005) applied the isohaline coordinate framework to investigate mixing in river plumes independently of the highly variable position of the plume.…”

Section: Introductionmentioning

confidence: 99%

A Universal Law of Estuarine Mixing

Burchard

2020

Journal of Physical Oceanography

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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) = S2Qr, where Qr is the average river runoff into the estuary. Consequently, the mixing per salinity class is m(S) = ∂SM(S) = 2SQr, 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.

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“…The theoretical framework based on a continuous salinity space was first developed by Walin (1977) and was later applied to exchange flow in the Baltic Sea (Walin, 1981). A comparable framework had been applied by Döös and Webb (1994) for quantifying meridional overturning circulation in the Southern Ocean. Both the bulk concept by Knudsen (1900) and the continuous concept by Walin (1977) had been consistently combined by MacCready (2011), who also coined the term TEF.…”

Section: Introductionmentioning

confidence: 99%

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

et al. 2019

Self Cite

View full text Add to dashboard Cite

Abstract. For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which uses salinity coordinates to calculate these bulk quantities, allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values for an increasing number of salinity classes. In the present study, this problem is investigated and the method of dividing salinities, described by MacCready et al. (2018), is mathematically introduced. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.

show abstract

Mixing Estimates for Estuaries

Cited by 23 publications

References 26 publications

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

A Universal Law of Estuarine Mixing

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

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