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

2019 ◽  
Author(s):  
Marvin Lorenz ◽  
Knut Klingbeil ◽  
Parker MacCready ◽  
Hans Burchard
Keyword(s):  
Original Method ◽  
Exchange Flow ◽  
Exact Formulation ◽  
Analysis Framework ◽  
The Baltic Sea ◽  
Exchange Flows ◽  
Estuarine Mixing ◽  
The Baltic ◽  
Estuarine Exchange ◽  
Total Exchange

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.

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

Ocean Science ◽  
2019 ◽  
Vol 15 (3) ◽  
pp. 601-614 ◽  
Author(s):  
Marvin Lorenz ◽  
Knut Klingbeil ◽  
Parker MacCready ◽  
Hans Burchard
Keyword(s):  
Original Method ◽  
Exchange Flow ◽  
Exact Formulation ◽  
Analysis Framework ◽  
The Baltic Sea ◽  
Exchange Flows ◽  
Estuarine Mixing ◽  
The Baltic ◽  
Estuarine Exchange ◽  
Total Exchange

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.

The Knudsen theorem and the Total Exchange Flow analysis framework applied to the Baltic Sea

2018 ◽  
Vol 165 ◽  
pp. 268-286 ◽  
Author(s):  
Hans Burchard ◽  
Karsten Bolding ◽  
Rainer Feistel ◽  
Ulf Gräwe ◽  
Knut Klingbeil ◽  
...  
Keyword(s):  
Baltic Sea ◽  
Flow Analysis ◽  
Exchange Flow ◽  
Analysis Framework ◽  
The Baltic Sea ◽  
The Baltic ◽  
Total Exchange

scholarly journals A Universal Law of Estuarine Mixing

2020 ◽  
Vol 50 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Hans Burchard
Keyword(s):  
River Runoff ◽  
Numerical Test ◽  
Test Cases ◽  
Exchange Flow ◽  
One Dimensional ◽  
Estuarine Mixing ◽  
Flow Mixing ◽  
Universal Law ◽  
Total Exchange

AbstractA 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.

scholarly journals Estuarine Exchange Flow Is Related to Mixing through the Salinity Variance Budget

2018 ◽  
Vol 48 (6) ◽  
pp. 1375-1384 ◽  
Author(s):  
Parker MacCready ◽  
W. Rockwell Geyer ◽  
Hans Burchard
Keyword(s):  
Steady State ◽  
3D Model ◽  
Exchange Flow ◽  
Volume Flux ◽  
Estuarine Exchange ◽  
The Relationship ◽  
Total Exchange

AbstractThe relationship between net mixing and the estuarine exchange flow may be quantified using a salinity variance budget. Here “mixing” is defined as the rate of destruction of volume-integrated salinity variance, and the exchange flow is quantified using the total exchange flow. These concepts are explored using an idealized 3D model estuary. It is shown that in steady state (e.g., averaging over the spring–neap cycle) the volume-integrated mixing is approximately given by Mixing ≅ SinSoutQr, where Sin and Sout are the representative salinities of in- and outflowing layers at the mouth and Qr is the river volume flux. This relationship provides an extension of the familiar Knudsen relation, in which the exchange flow is diagnosed based on knowledge of these same three quantities, quantitatively linking mixing to the exchange flow.

Dynamics of the Baltic Sea straits via numerical simulation of exchange flows

2018 ◽  
Vol 131 ◽  
pp. 40-58 ◽  
Author(s):  
E.V. Stanev ◽  
J. Pein ◽  
S. Grashorn ◽  
Y. Zhang ◽  
C. Schrum
Keyword(s):  
Numerical Simulation ◽  
Baltic Sea ◽  
The Baltic Sea ◽  
Exchange Flows ◽  
Sea Straits ◽  
The Baltic

scholarly journals Tracing inputs of terrestrial high molecular weight dissolved organic matter within the Baltic Sea ecosystem

2012 ◽  
Vol 9 (11) ◽  
pp. 4465-4475 ◽  
Author(s):  
B. Deutsch ◽  
V. Alling ◽  
C. Humborg ◽  
F. Korth ◽  
C. M. Mörth
Keyword(s):  
Molecular Weight ◽  
Organic Matter ◽  
Dissolved Organic Matter ◽  
Baltic Sea ◽  
High Molecular Weight ◽  
Salinity Gradient ◽  
The Baltic Sea ◽  
Estuarine Mixing ◽  
The Baltic ◽  
Bothnian Bay

Abstract. To test the hypothesis whether high molecular weight dissolved organic matter (HMW-DOM) in a high latitude marginal sea is dominated by terrestrial derived matter, 10 stations were sampled along the salinity gradient of the central and northern Baltic Sea and were analyzed for concentrations of dissolved organic carbon as well as δ13C values of HMW-DOM. Different end-member-mixing models were applied to quantify the influence of terrestrial DOM and to test for conservative versus non-conservative behavior of the terrestrial DOM in the different Baltic Sea basins. The share of terrestrial DOM to the total HMW-DOM was calculated for each station, ranging from 43 to 83%. This shows the high influence of terrestrial DOM inputs for the Baltic Sea ecosystem. The data also suggest that terrestrial DOM reaching the open Baltic Sea is not subject to substantial removal anymore. However compared to riverine DOM concentrations, our results indicate that substantial amounts of HMW-DOM (> 50%) seem to be removed near the coastline during estuarine mixing. A budget approach yielded residence times for terrestrial DOM of 2.8, 3.0, and 4.5 yr for the Bothnian Bay, the Bothnian Sea and the Baltic Proper.

Influence of Lateral Advection on Residual Currents in Microtidal Estuaries

2009 ◽  
Vol 39 (12) ◽  
pp. 3177-3190 ◽  
Author(s):  
Peng Cheng ◽  
Arnoldo Valle-Levinson
Keyword(s):  
Vertical Mixing ◽  
Earth’S Rotation ◽  
Scaling Analysis ◽  
Main Role ◽  
Exchange Flow ◽  
Earth's Rotation ◽  
Estuarine Dynamics ◽  
Exchange Flows ◽  
Estuarine Exchange ◽  
Lateral Advection

Abstract The influence of nonlinear lateral advection on estuarine exchange flow is examined with a scaling analysis and eight groups of idealized numerical experiments. Nonlinear lateral advection is related to the linkage between lateral circulation and the lateral shear of the along-estuary flow. The relative contribution of lateral advection to the overall dynamics of a microtidal estuary is found to be a function of width and depth, and of vertical mixing. Lateral advection is dynamically important in narrow and deep estuaries, particularly under relatively weak vertical mixing. The relative importance of lateral advection and the earth’s rotation on estuarine dynamics can be evaluated in terms of the nondimensional Rossby and Ekman numbers (Ro and Ek). Lateral advection is most effective at large Ro and small Ek and is negligible at small Ro and large Ek. As expected, the earth’s rotation is most significant at small Ro and Ek, and is negligible at large Ro and Ek. Under the influence of lateral advection and the earth’s rotation, the lateral structure of estuarine exchange flows is a function of Ro and Ek. In some instances, the exchange flow is vertically sheared and in others it is laterally sheared. Classical estuarine dynamics, which yields vertically sheared exchange flows, occurs at intermediate Ro and large Ek. The main role of lateral advection is to reduce lateral variability of estuarine exchange flow and generate a vertically sheared, two-layer exchange flow structure.

scholarly journals Tracing inputs of terrestrial high molecular weight dissolved organic matter within the Baltic Sea Ecosystem

2012 ◽  
Vol 9 (4) ◽  
pp. 4483-4512 ◽  
Author(s):  
B. Deutsch ◽  
V. Alling ◽  
C. Humborg ◽  
F. Korth ◽  
C. M. Mörth
Keyword(s):  
Molecular Weight ◽  
Organic Matter ◽  
Dissolved Organic Matter ◽  
Baltic Sea ◽  
High Molecular Weight ◽  
Salinity Gradient ◽  
The Baltic Sea ◽  
Estuarine Mixing ◽  
The Baltic ◽  
Bothnian Bay

Abstract. To test the hypothesis whether dissolved organic matter (DOM) in a high latitude marginal sea is dominated by terrestrial derived matter 10 stations were sampled along the salinity gradient of the central and northern Baltic Sea and were analyzed for concentrations of dissolved organic carbon as well as δ13C values of high molecular weight DOM. Different end-member-mixing models were applied to quantify the influence of terrestrial DOM and to test for conservative versus non-conservative behavior of the terrestrial dissolved organic matter in the different Baltic Sea basins. The share of terrestrial DOM to the total DOM was calculated for each station, ranging from 43 to 83%. This shows the high influence of terrestrial DOM inputs for the Baltic Sea ecosystem. The data also suggest that terrestrial DOM that reaches the open Baltic Sea is not subject to substantial removal anymore. However compared to riverine DOM concentrations our results indicate that substantial amounts of DOM (>50%) seems to be removed near the coastline during estuarine mixing. A budget approach yielded residence times for terrestrial DOM of 2.3, 2.7, and 4.1 yr for the Bothnian Bay, the Bothnian Sea and the Baltic Proper.

scholarly journals Calculating Estuarine Exchange Flow Using Isohaline Coordinates*

2011 ◽  
Vol 41 (6) ◽  
pp. 1116-1124 ◽  
Author(s):  
Parker MacCready
Keyword(s):  
Residence Time ◽  
River Estuary ◽  
Columbia River ◽  
Time Dependent ◽  
Salt Flux ◽  
Exchange Flow ◽  
Exact Formulation ◽  
Volume Flux ◽  
Columbia River Estuary ◽  
Estuarine Exchange

Abstract A method for calculating subtidal estuarine exchange flow using an isohaline framework is described, and the results are compared with those of the more commonly used Eulerian method of salt flux decomposition. Concepts are explored using a realistic numerical simulation of the Columbia River estuary. The isohaline method is found to be advantageous because it intrinsically highlights the salinity classes in which subtidal volume flux occurs. The resulting expressions give rise to an exact formulation of the time-dependent Knudsen relation and may be used in calculation of the saltwater residence time. The volume flux of the landward transport, which can be calculated precisely using the isohaline framework, is of particular importance for problems in which the saltwater residence time is critical.

scholarly journals The Model to Assess the Implementation of Technical Conditions Defined in Annex IV of Marpol Convention 73/78: The Case of the Baltic Sea Port of Klaipeda

2016 ◽  
Vol 17 (4) ◽  
pp. 335-349
Author(s):  
Andrius Jarzemskis ◽  
Ilona Jarzemskiene
Keyword(s):  
Baltic Sea ◽  
Marine Environment ◽  
Environment Protection ◽  
Analysis Framework ◽  
The Baltic Sea ◽  
Eu Directive ◽  
Passenger Ships ◽  
Framework Model ◽  
The Baltic ◽  
Protection Commission

Abstract Baltic Marine Environment Protection Commission members seeking to implement MARPOL 73/78 Annex IV amendments which recognize the Baltic Sea as special are, in which discharge of uncommitted sewage from passenger ships is forbidden, must ensure that ports are equipped with adequate reception facilities. To ensure implementation of amendments of Annex IV in port of Klaipeda, the analysis framework model was defined by authors. The model evaluates the readiness of the port to changes brought by the amendments of MARPOL Annex IV. The scientific problem comes with perception of adequacy. Resolution MEPC.200(62) amending MARPOL 73/78 Annex IV states, that port reception facilities must be adequate to the needs of passenger ships using them without causing undue delay. Concept of adequacy is not defined, therefore other guidelines explaining adequacy were used: EU directive 2000/59/EC and IMO resolution MEPC.83(44) Guidelines for ensuring adequacy of port reception facilities. Based on these sources, criteria that must be met to ensure adequacy were identified and tested in article: 1) reception facilities meet needs of ships normally using them; 2) discharge of sewage does to cause undue delay; 3) reception facilities does not provide disincentive to use them; 4) facilities are accessible; 5) facilities contribute to the improvement of the marine environment.

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