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1. Estuarine Circulation, Mixing, and Residence Times in the Salish Sea

   https://doi.org/10.1029/2020JC016738  

   MacCready, P.; McCabe, R. M.; Siedlecki, S. A.; Lorenz, M.; Giddings, S. N.; Bos, J.; Albertson, S.; Banas, N. S.; Garnier, S. (February 2021, Journal of Geophysical Research: Oceans)

   Abstract A realistic numerical model is used to study the circulation and mixing of the Salish Sea, a large, complex estuarine system on the United States and Canadian west coast. The Salish Sea is biologically productive and supports many important fisheries but is threatened by recurrent hypoxia and ocean acidification, so a clear understanding of its circulation patterns and residence times is of value. The estuarine exchange flow is quantified at 39 sections over 3 years (2017–2019) using the Total Exchange Flow method. Vertical mixing in the 37 segments between sections is quantified as opposing vertical transports: the efflux and reflux. Efflux refers to the rate at which deep, landward‐flowing water is mixed up to become part of the shallow, seaward‐flowing layer. Similarly, reflux refers to the rate at which upper layer water is mixed down to form part of the landward inflow. These horizontal and vertical transports are used to create a box model to explore residence times in a number of different sub‐volumes, seasons, and years. Residence times from the box model are generally found to be longer than those based on simpler calculations of flushing time. The longer residence times are partly due to reflux, and partly due to incomplete tracer homogenization in sub‐volumes. The methods presented here are broadly applicable to other estuaries. 

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2. Reversed Lateral Circulation in a Sharp Estuarine Bend with Weak Stratification

   https://doi.org/10.1175/JPO-D-18-0175.1  

   Kranenburg, Wouter M.; Geyer, W. Rockwell; Garcia, Adrian Mikhail; Ralston, David K. (June 2019, Journal of Physical Oceanography)
3. Lateral Transport Controls the Tidally Averaged Gravitationally Driven Estuarine Circulation: Tidal Mixing Effects

   https://doi.org/10.1175/JPO-D-23-0221.1  

   Kukulka, Tobias; Chant, Robert J (August 2024, Journal of Physical Oceanography)

   Abstract In classic models of the tidally averaged gravitationally driven estuarine circulation, denser salty oceanic water moves up the estuary near the bottom, while less dense riverine water flows toward the ocean near the surface. Traditionally, it is assumed that the associated pressure gradient forces and salt advection are balanced by vertical mixing. This study, however, demonstrates that lateral (across the estuary width) transport processes are essential for maintaining the estuarine circulation. This is because for realistic estuarine bathymetry, the depth-integrated salt transport up the estuary is enhanced in the deeper estuary channel. A closed salt budget then requires the lateral transport of this excess salt in the deeper channel toward the estuarine flanks. To understand how such lateral transport affects the estuarine salt and momentum balances, we devise an idealized model with explicit lateral transport focusing on tidally averaged lateral mixing effects. Solutions for the along-estuary velocity and salinity are nondimensionalized to depend only on one single nondimensional parameter, referred to as the Fischer number, which describes the relative importance of lateral to vertical tidal mixing. For relatively strong lateral tidal mixing (greater Fischer number), salinity and velocity variations are predominantly vertical. For relatively weak lateral tidal mixing (smaller Fischer number), salinity and velocity variations are predominantly lateral. Overall, lateral transport greatly affects the estuarine circulation and controls the estuarine salinity intrusion length, which is demonstrated to scale inversely with the Fischer number. 

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

   https://doi.org/10.5194/os-15-601-2019  

   Lorenz, Marvin; Klingbeil, Knut; MacCready, Parker; Burchard, Hans (January 2019, Ocean Science)

   Abstract. For more than a century, estuarine exchange flow has been quantified by meansof the Knudsen relations which connect bulk quantities such as inflow andoutflow volume fluxes and salinities. These relations are closely linked toestuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which usessalinity coordinates to calculate these bulk quantities, allows an exactformulation of the Knudsen relations in realistic cases. There are howevernumerical issues, since the original method does not converge to the TEF bulkvalues 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. Achallenging yet compact analytical scenario for a well-mixed estuarineexchange flow is investigated for both methods, showing the properconvergence of the dividing salinity method. Furthermore, the dividingsalinity method is applied to model results of the Baltic Sea to demonstratethe analysis of realistic exchange flows and exchange flows with more thantwo layers. 

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5. Estuarine Exchange Flow in the Albemarle‐Pamlico Estuarine System

   https://doi.org/10.1029/2024JC021919  

   Yin, Dongxiao; Harris, Courtney_K; Warner, John_C (August 2025, Journal of Geophysical Research: Oceans)

   Abstract Estuarine exchange flow controls the salt balance and regulates biogeochemistry in an estuary. The Albemarle‐Pamlico estuarine system (APES) is the largest coastal lagoon in the U.S. and historically susceptible to a series of environmental issues including salt water intrusion and eutrophication, yet its estuarine exchange flow is poorly understood. Here, we investigate the estuarine exchange flow in the APES, its tributary estuaries (Pamlico and Neuse), and sub‐basin Albemarle Sound using the total exchange flow analysis framework based on results from a deterministic numerical model. We find the following: (a) Dynamics controlling estuarine exchange flow in the APES vary spatially and depend on timescales considered. At inlets, estuarine exchange flows respond to both tidal prism and residual water levels at weather‐to‐spring/neap timescales. At a long quasi‐steady timescale represented as annual means, estuarine exchange flow is dominated by barotropic flow. Within the tributary estuaries, estuarine exchange flows at timescales of wind periods are controlled by wind‐induced straining, whereas the quasi‐steady state condition is dominated by gravitational circulation. At Albemarle Sound, exchange flow is dominated by the residual water levels at weather‐to‐spring/neap timescales, while at quasi‐steady state it is controlled by barotropic flow. (b) At the quasi‐steady annual timescale, the salt content decreases with river discharge. At the weather‐to‐spring/neap timescales, salt content is insensitive to variations in estuarine exchange flow, except for within Albemarle Sound. (c) Estuarine exchange flow likely influences the biogeochemistry of the APES by playing a key role in regulating the flushing efficiency and material exchange, a role that has been previously overlooked. 

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