Total Exchange Flow, Entrainment, and Diffusive Salt Flux in Estuaries

AbstractThe linkage among total exchange flow, entrainment, and diffusive salt flux in estuaries is derived analytically using salinity coordinates, revealing the simple but important relationship between total exchange flow and mixing. Mixing is defined and quantified in this paper as the dissipation of salinity variance. The method uses the conservation of volume and salt to quantify and distinguish the diahaline transport of volume (i.e., entrainment) and diahaline diffusive salt flux. A numerical model of the Hudson estuary is used as an example of the application of the method in a realistic estuary with a persistent but temporally variable exchange flow. A notable finding of this analysis is that the total exchange flow and diahaline salt flux are out of phase with respect to the spring–neap cycle. Total exchange flow reaches its maximum near minimum neap tide, but diahaline salt transport reaches its maximum during the maximum spring tide. This phase shift explains the strong temporal variation of stratification and estuarine salt content through the spring–neap cycle. In addition to quantifying temporal variation, the method reveals the spatial variation of total exchange flow, entrainment, and diffusive salt flux through the estuary. For instance, the analysis of the Hudson estuary indicates that diffusive salt flux is intensified in the wider cross sections. The method also provides a simple means of quantifying numerical mixing in ocean models because it provides an estimate of the total dissipation of salinity variance, which is the sum of mixing due to the turbulence closure and numerical mixing.

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Estuarine Exchange Flow Quantified with Isohaline Coordinates: Contrasting Long and Short Estuaries

Journal of Physical Oceanography ◽

10.1175/jpo-d-11-086.1 ◽

2012 ◽

Vol 42 (5) ◽

pp. 748-763 ◽

Cited By ~ 27

Author(s):

Shih-Nan Chen ◽

W. Rockwell Geyer ◽

David K. Ralston ◽

James A. Lerczak

Keyword(s):

Pressure Gradient ◽

Tidal Volume ◽

Numerical Models ◽

Physical Space ◽

Hudson River ◽

Salt Transport ◽

Salt Flux ◽

Exchange Flow ◽

Volume Flux ◽

Tidal Excursion

Abstract Isohaline coordinate analysis is used to compare the exchange flow in two contrasting estuaries, the long (with respect to tidal excursion) Hudson River and the short Merrimack River, using validated numerical models. The isohaline analysis averages fluxes in salinity space rather than in physical space, yielding the isohaline exchange flow that incorporates both subtidal and tidal fluxes and precisely satisfies the Knudsen relation. The isohaline analysis can be consistently applied to both subtidally and tidally dominated estuaries. In the Hudson, the isohaline exchange flow is similar to results from the Eulerian analysis, and the conventional estuarine theory can be used to quantify the salt transport based on scaling with the baroclinic pressure gradient. In the Merrimack, the isohaline exchange flow is much larger than the Eulerian quantity, indicating the dominance of tidal salt flux. The exchange flow does not scale with the baroclinic pressure gradient but rather with tidal volume flux. This tidal exchange is driven by tidal pumping due to the jet–sink flow at the mouth constriction, leading to a linear dependence of exchange flow on tidal volume flux. Finally, a tidal conversion parameter Qin/Qprism, measuring the fraction of tidal inflow Qprism that is converted into net exchange Qin, is proposed to characterize the exchange processes among different systems. It is found that the length scale ratio between tidal excursion and salinity intrusion provides a characteristic to distinguish estuarine regimes.

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Mechanisms of Tidal Oscillatory Salt Transport in a Partially Stratified Estuary

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0031.1 ◽

2015 ◽

Vol 45 (11) ◽

pp. 2773-2789 ◽

Cited By ~ 8

Author(s):

Tao Wang ◽

W. Rockwell Geyer ◽

Patricia Engel ◽

Wensheng Jiang ◽

Shizuo Feng

Keyword(s):

Spring Tide ◽

Vertical Mixing ◽

Oscillatory Shear ◽

Salt Transport ◽

Exchange Flow ◽

Advective Transport ◽

Tidal Variation ◽

Shear Dispersion ◽

Large Channel ◽

Stratified Estuary

AbstractTidal oscillatory salt transport, induced by the correlation between tidal variations in salinity and velocity, is an important term for the subtidal salt balance under the commonly used Eulerian method of salt transport decomposition. In this paper, its mechanisms in a partially stratified estuary are investigated with a numerical model of the Hudson estuary. During neap tides, when the estuary is strongly stratified, the tidal oscillatory salt transport is mainly due to the hydraulic response of the halocline to the longitudinal variation of topography. This mechanism does not involve vertical mixing, so it should not be regarded as oscillatory shear dispersion, but instead it should be regarded as advective transport of salt, which results from the vertical distortion of exchange flow obtained in the Eulerian decomposition by vertical fluctuations of the halocline. During spring tides, the estuary is weakly stratified, and vertical mixing plays a significant role in the tidal variation of salinity. In the spring tide regime, the tidal oscillatory salt transport is mainly due to oscillatory shear dispersion. In addition, the transient lateral circulation near large channel curvature causes the transverse tilt of the halocline. This mechanism has little effect on the cross-sectionally integrated tidal oscillatory salt transport, but it results in an apparent left–right cross-channel asymmetry of tidal oscillatory salt transport. With the isohaline framework, tidal oscillatory salt transport can be regarded as a part of the net estuarine salt transport, and the Lagrangian advective mechanism and dispersive mechanism can be distinguished.

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Circulation and salt balance in the São Francisco river Estuary (NE/Brazil)

RBRH ◽

10.1590/2318-0331.021720170003 ◽

2017 ◽

Vol 22 (0) ◽

Cited By ~ 4

Author(s):

Geórgenes Cavalcante ◽

Luiz Bruner de Miranda ◽

Paulo Ricardo Petter Medeiros

Keyword(s):

River Discharge ◽

Neap Tide ◽

Spring Tide ◽

River Estuary ◽

Salt Transport ◽

Salt Flux ◽

Sao Francisco River ◽

Tidal Cycles ◽

São Francisco River ◽

And Diffusion

ABSTRACT In order to evaluate how river discharge and tidal currents forcing influence the circulation and salt transport within the São Francisco River-Estuary, a two 25 hour surveys campaigns and along-channel profiles were performed in the estuary main channel (18/19 and 25/26 February 2014). The current intensity showed higher asymmetry between flood (v<0) and ebb (v>0) currents in spring tide (-0.6 and 1.1 m/s), as compared to neap tide (-0.4 and 1.0 m/s), which was attributed to the intense buoyancy energy enhanced by the stronger discharge in spring. Overall, salinity presented high stratified conditions and varied between 0.0<S<36.6, and 0.5<S<36.1 from surface to bottom, during spring and neap, respectively. Although river discharge reduced from spring to neap tide partially mixed-highly stratified conditions (type 2b) remained in both periods, with advection and diffusion contributing with 34% and 66% to the net upstream salt flux in spring, respectively, and 56% and 44% in neap tide, respectively, which was attributed to the balance of tidal and baroclinic forcing and river discharge. The dominant downstream advective salt transport in both spring (12.5 kg.m-1s-1) and neap (15.2 kg.m-1s-1) tidal cycles suggests that there is little salt accumulation inside the São Francisco estuary.

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Mixing Estimates for Estuaries

Journal of Physical Oceanography ◽

10.1175/jpo-d-18-0147.1 ◽

2019 ◽

Vol 49 (2) ◽

pp. 631-648 ◽

Cited By ~ 5

Author(s):

Hans Burchard ◽

Xaver Lange ◽

Knut Klingbeil ◽

Parker MacCready

Keyword(s):

Turbulent Mixing ◽

Tidal Flow ◽

Salt Flux ◽

Open Boundary ◽

Test Cases ◽

Exchange Flow ◽

Analysis Framework ◽

Estuarine Mixing ◽

Numerical Mixing ◽

Diffusive Fluxes

AbstractThe well-known Knudsen relations and the total exchange flow (TEF) analysis framework provide quantifications of exchange flow across an open boundary to the adjacent ocean in terms of bulk values (Knudsen theory: inflow and outflow volume or salinity) or with resolution in salinity space (TEF: profiles of volume and salt flux in salinity coordinates). In the present study, these theories are extended toward mixing of salinity, 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 first one is exact and considers nonperiodicity as well as nonconstancy of the inflow and outflow salinities. The other three formulations are approximate only, in the sense that either nonperiodicity or nonconstancy or both are relaxed. The simplest of those formulations has recently been derived by MacCready et al. and estimates the estuarine mixing as the product of inflow salinity, outflow salinity, and time-averaged river runoff. These 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 (physical plus numerical) mixing within an error of about 10%.

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Fluvial modulation of hydrodynamics and salt transport in a highly stratified estuary

Brazilian Journal of Oceanography ◽

10.1590/s1679-87592010000200007 ◽

2010 ◽

Vol 58 (2) ◽

pp. 165-175 ◽

Cited By ~ 4

Author(s):

Carla de Abreu D'Aquino ◽

Jurandir Pereira Filho ◽

Carlos Augusto França Schettini

Keyword(s):

Time Series ◽

Water Level ◽

River Discharge ◽

Spring Tide ◽

River Estuary ◽

Salt Transport ◽

Salt Flux ◽

Rain Event ◽

Stratified Estuary ◽

A Site

An oceanographic campaign was conducted in the Araranguá river estuary during the period from May 11th to 13th of 2006 in order to produce a first hydrographic characterization of this system. The campaign was carried out during the spring tide period, and coincidentally after an intense rain event in the region which produced a peak in river discharge. Water level, currents and salinity time series were recorded hourly during a 50-hour period, at a site nearly 7 km upstream from the estuarine mouth. Two longitudinal distributions of salinity along the estuary were also recorded. The hydrographic data time-series were used to compute the advective salt flux in order to investigate the changes in the transport terms as a function of the change in discharge. The results showed that the estuarine structure was strongly modulated by the river discharge. The drop in water level of about 0.5 m during the first 24 hours was directly related to the ebb phase of the river flood. The water column was highly stratified throughout the period, therefore the stratification increased during the last 24 hours. The currents were stronger, ebbing and uni-directional at the beginning and became weaker and bidirectional as the water level went down, assuming a tidal pattern. The total salt transport in the first 25 hours was of -13.6 kg.m-1.s-1 (seawards), decreasing to 3 Kg.m-1.s-1 during the last 25 hours (landwards). It was also noticeable that the pH in the estuary, recorded together with the salinity, was around 5, showing that the water quality in the estuary is affected by the coal mining activity in the hydrographic basin.

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Asymmetric Estuarine Responses to Changes in River Forcing: A Consequence of Nonlinear Salt Flux

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0085.1 ◽

2015 ◽

Vol 45 (11) ◽

pp. 2836-2847 ◽

Cited By ~ 6

Author(s):

Shih-Nan Chen

Keyword(s):

Response Time ◽

Linear Theory ◽

Nonlinear Effect ◽

Nonlinear Function ◽

Power Laws ◽

Salt Transport ◽

Salt Flux ◽

Exchange Flow ◽

Salinity Field ◽

The Asymmetry

AbstractA linear theory for estuarine adjustment to river forcing as put forth by MacCready is extended to allow for quantification of nonlinear salt flux induced by gravitational exchange flow. It has been shown that, under a steplike change of river forcing, the estuarine responses are asymmetric, with the salinity field adjusting faster during the rising discharge. The asymmetry arises because the up-estuary salt flux due to exchange flow is a nonlinear function of estuarine length ∝ L−3. During the rising discharge, the estuary is longer, and the salt flux is comparatively less sensitive to the length variations. As a result, the up-estuary salt transport cannot keep pace with the rate of discharge changes, leading to a larger net salt flux and thus a shorter response time. A simple theory accounting for the nonlinear effect is then applied to Hudson-like systems and shown to capture the asymmetric response. The asymmetry is generalizable to other estuarine regimes where up-estuary salt fluxes are expressed as nonlinear power laws.

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A Numerical Study of Salt Fluxes in Delaware Bay Estuary

Journal of Physical Oceanography ◽

10.1175/jpo-d-12-0124.1 ◽

2013 ◽

Vol 43 (8) ◽

pp. 1572-1588 ◽

Cited By ~ 18

Author(s):

María Aristizábal ◽

Robert Chant

Keyword(s):

River Discharge ◽

Neap Tide ◽

Numerical Study ◽

Spring Tide ◽

Delaware Bay ◽

Salt Flux ◽

Exchange Flow ◽

Regional Ocean Modeling System ◽

Salinity Field ◽

Estuarine Exchange

Abstract The results of a numerical study of Delaware Bay using the Regional Ocean Modeling System (ROMS) are presented. The simulations are run over a range of steady river inputs and used M2 and S2 tidal components to capture the spring–neap variability. Results provide a description of the spatial and temporal structure of the estuarine exchange flow and the salinity field, as well the along-channel salt flux in the estuary. The along-channel salt flux is decomposed into an advective term associated with the river flow, a steady shear dispersion Fe associated with the estuarine exchange flow, and a tidal oscillatory salt flux Ft. Time series of Fe and Ft show that both are larger during neap tide than during spring. This time variability of Ft, which is contrary to existing scalings, is caused by the lateral flows that bring velocity and salinity out of quadrature and the stronger stratification during neap tide, which causes Ft to be enhanced relative to spring tide. A fit for the salt intrusion length L with river discharge Q for a number of isohalines is performed. The functional dependences of L with Q are significantly weaker than Q−1/3 scaling. It is concluded that the response of the salt field with river discharge is due to the dependence of Fe and Ft with Q and the relative importance of Ft to the total upstream salt flux: as river discharge increases, Fe becomes the dominant mechanism. Once Fe dominates, the salt field stiffens because of a reduction of the vertical eddy viscosity with increasing Q.

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Glomerulotubular balance in a mathematical model of the proximal nephron

AJP Renal Physiology ◽

10.1152/ajprenal.1990.258.3.f612 ◽

1990 ◽

Vol 258 (3) ◽

pp. F612-F626 ◽

Cited By ~ 4

Author(s):

A. M. Weinstein

Keyword(s):

Tight Junction ◽

Proximal Tubule ◽

Water Permeability ◽

Water Flux ◽

Salt Transport ◽

Salt Flux ◽

Filtration Fraction ◽

Epithelial Junctions ◽

Permeability Increase ◽

Glomerulotubular Balance

A nonelectrolyte model of proximal tubule epithelium has been extended by the inclusion of a compliant tight junction. Here "compliance" signifies that both the junctional salt and water permeability increase and the salt reflection coefficient decreases in response to small pressure differences from lateral interspace to tubule lumen. In previous models of rat proximal tubule, there has been virtually no sensitivity of isotonic salt transport to changes in peritubular oncotic force. With the inclusion of junctional compliance, decreases in peritubular protein can open the junction and produce a secretory salt flux. Thus the model can represent the "backflux hypothesis," as it was originally put forth (J. E. Lewy and E. E. Windhager, Am. J. Physiol. 214: 943-954, 1968). Additional calculations, simulating a tight junction with negligible water permeability, reveal that the quantitative impact of peritubular protein can be realized whether or not there is substantial junctional water flux. The epithelial model of proximal tubule has also been incorporated into a model of the proximal nephron, complete with glomerulus, peritubular capillary, and interstitium. The interstitial compartment is well mixed and interstitial pressure and osmolality are determined iteratively to achieve balance between tubule reabsorption and capillary uptake. For this model, two domains of operation are identified. When interstitial pressures are low, junctions are closed, and filtration fraction has no effect on proximal reabsorption. When interstitial pressures are relatively elevated, epithelial junctions are open, and proximal salt reabsorption changes in proportion to changes in filtration fraction. In neither domain, however, does the model tubule augment salt flux with isolated increases in luminal flow rate (at constant filtration fraction). The absence of a separate effect of tubule fluid flow on salt transport precludes perfect glomerulotubular balance.

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Using an Isohaline Flux Analysis to Predict the Salt Content in an Unsteady Estuary

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0134.1 ◽

2017 ◽

Vol 47 (11) ◽

pp. 2811-2828 ◽

Cited By ~ 4

Author(s):

Matthew D. Rayson ◽

Edward S. Gross ◽

Robert D. Hetland ◽

Oliver B. Fringer

Keyword(s):

River Flow ◽

Salt Content ◽

Box Model ◽

Flux Analysis ◽

Galveston Bay ◽

Exchange Flow ◽

Salt Intrusion ◽

Adjustment Time ◽

The Mean ◽

Salinity Difference

AbstractAn estuary is classified as unsteady when the salinity adjustment time is longer than the forcing time scale. Predicting salt content or salt intrusion length using scaling arguments based on a steady-state relationship between flow and salinity is inaccurate in these systems. In this study, a time-dependent salinity box model based on an unsteady Knudsen balance is used to demonstrate the effects of river flow, inward total exchange flow (tidal plus steady), and the salinity difference between inflow and outflow on the salt balance. A key component of the box model is a relationship that links the normalized difference between inflowing and outflowing salinity at the mouth and the mean salinity content. The normalized salinity difference is shown to be proportional to the mean salinity squared, based on theoretical arguments from the literature. The box model is validated by hindcasting 5 years of mean salinity in Galveston Bay (estimated from coarse observations) in response to highly variable river discharge. It is shown that this estuary typically has a long adjustment time relative to the forcing time scales, and, therefore, the volume-averaged salinity rarely reaches equilibrium. The box model highlights the reasons why the adjustment time in a large, partially mixed estuary like Galveston Bay is slower when the mean salt content is higher. Furthermore, it elucidates why the salt content in the estuary is more responsive to changes in river flow than in landward exchange flow at the estuary mouth, even though the latter quantity is usually several times larger.

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