Salt Dynamics in Well-Mixed Estuaries: Importance of Advection by Tides

Xiaoyan Wei Applied Mathematics, Delft University of Technology, Delft, Netherlands

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George P. Schramkowski Flanders Hydraulics Research, Antwerp, Belgium

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Henk M. Schuttelaars Applied Mathematics, Delft University of Technology, Delft, Netherlands

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Abstract

Understanding salt dynamics is important to adequately model salt intrusion, baroclinic forcing, and sediment transport. In this paper, the importance of the residual salt transport due to tidal advection in well-mixed tidal estuaries is studied. The water motion is resolved in a consistent way with a width-averaged analytical model, coupled to an advection–diffusion equation describing the salt dynamics. The residual salt balance obtained from the coupled model shows that the seaward salt transport driven by river discharge is balanced by the landward salt transport due to tidal advection and horizontal diffusion. It is found that the tidal advection behaves as a diffusion process, and this contribution is named tidal advective diffusion. The horizontal diffusion parameterizes processes not explicitly resolved in the model and is called the prescribed diffusion. The tidal advective diffusion results from the correlation between the tidal velocity and salinity and can be explicitly calculated with the dominant semidiurnal water motion. The sensitivity analysis shows that tidal advective diffusivity increases with increasing bed roughness and decreasing vertical eddy viscosity. Furthermore, tidal advective diffusivity reaches its maximum for moderate water depth and moderate convergence length. The relative importance of tidal advective diffusion is investigated using the residual salt balance, with the prescribed diffusion coefficient obtained from the measured salinity field. The tidal advective diffusion dominates the residual salt transport in the Scheldt estuary, and other processes significantly contribute to the residual salt transport in the Delaware estuary and the Columbia estuary.

Corresponding author address: Xiaoyan Wei, Delft University of Technology, Mekelweg 4, 2624 CD, Delft, Netherlands. E-mail: xywei1988@hotmail.com

Abstract

Understanding salt dynamics is important to adequately model salt intrusion, baroclinic forcing, and sediment transport. In this paper, the importance of the residual salt transport due to tidal advection in well-mixed tidal estuaries is studied. The water motion is resolved in a consistent way with a width-averaged analytical model, coupled to an advection–diffusion equation describing the salt dynamics. The residual salt balance obtained from the coupled model shows that the seaward salt transport driven by river discharge is balanced by the landward salt transport due to tidal advection and horizontal diffusion. It is found that the tidal advection behaves as a diffusion process, and this contribution is named tidal advective diffusion. The horizontal diffusion parameterizes processes not explicitly resolved in the model and is called the prescribed diffusion. The tidal advective diffusion results from the correlation between the tidal velocity and salinity and can be explicitly calculated with the dominant semidiurnal water motion. The sensitivity analysis shows that tidal advective diffusivity increases with increasing bed roughness and decreasing vertical eddy viscosity. Furthermore, tidal advective diffusivity reaches its maximum for moderate water depth and moderate convergence length. The relative importance of tidal advective diffusion is investigated using the residual salt balance, with the prescribed diffusion coefficient obtained from the measured salinity field. The tidal advective diffusion dominates the residual salt transport in the Scheldt estuary, and other processes significantly contribute to the residual salt transport in the Delaware estuary and the Columbia estuary.

Corresponding author address: Xiaoyan Wei, Delft University of Technology, Mekelweg 4, 2624 CD, Delft, Netherlands. E-mail: xywei1988@hotmail.com
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  • Aristizábal, M., and R. Chant, 2013: A numerical study of salt fluxes in Delaware Bay estuary. J. Phys. Oceanogr., 43, 15721588, doi:10.1175/JPO-D-12-0124.1.

    • Search Google Scholar
    • Export Citation
  • Bowen, M. M., and W. R. Geyer, 2003: Salt transport and the time-dependent salt balance of a partially stratified estuary. J. Geophys. Res., 108, 3158, doi:10.1029/2001JC001231.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., and H. Baumert, 1998: The formation of estuarine turbidity maxima due to density effects in the salt wedge. A hydrodynamic process study. J. Phys. Oceanogr., 28, 309321, doi:10.1175/1520-0485(1998)028<0309:TFOETM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., and R. D. Hetland, 2010: Quantifying the contributions of tidal straining and gravitational circulation to residual circulation in periodically stratified tidal estuaries. J. Phys. Oceanogr., 40, 12431262, doi:10.1175/2010JPO4270.1.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., R. D. Hetland, E. Schulz, and H. M. Schuttelaars, 2011: Drivers of residual estuarine circulation in tidally energetic estuaries: Straight and irrotational channels with parabolic cross section. J. Phys. Oceanogr., 41, 548570, doi:10.1175/2010JPO4453.1.

    • Search Google Scholar
    • Export Citation
  • Cheng, P., A. Valle-Levinson, and H. E. De Swart, 2010: Residual currents induced by asymmetric tidal mixing in weakly stratified narrow estuaries. J. Phys. Oceanogr., 40, 21352147, doi:10.1175/2010JPO4314.1.

    • Search Google Scholar
    • Export Citation
  • Chernetsky, A. S., H. M. Schuttelaars, and S. A. Talke, 2010: The effect of tidal asymmetry and temporal settling lag on sediment trapping in tidal estuaries. Ocean Dyn., 60, 12191241, doi:10.1007/s10236-010-0329-8.

    • Search Google Scholar
    • Export Citation
  • Davies, A., and J. Jones, 1996: Sensitivity of tidal bed stress distributions, near-bed currents, overtides, and tidal residuals to frictional effect in the eastern Irish Sea. J. Phys. Oceanogr., 26, 25532575, doi:10.1175/1520-0485(1996)026<2553:SOTBSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fischer, H., 1972: Mass transport mechanisms in partially stratified estuaries. J. Fluid Mech., 53, 671687, doi:10.1017/S0022112072000412.

    • Search Google Scholar
    • Export Citation
  • Friedrichs, C. T., and D. G. Aubrey, 1994: Tidal propagation in strongly convergent channels. J. Geophys. Res., 99, 33213336, doi:10.1029/93JC03219.

    • Search Google Scholar
    • Export Citation
  • Garvine, R. W., R. K. McCarthy, and K.-C. Wong, 1992: The axial salinity distribution in the Delaware estuary and its weak response to river discharge. Estuarine Coastal Shelf Sci., 35, 157165, doi:10.1016/S0272-7714(05)80110-6.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., and P. MacCready, 2014: The estuarine circulation. Annu. Rev. Fluid Mech., 46, 175197, doi:10.1146/annurev-fluid-010313-141302.

    • Search Google Scholar
    • Export Citation
  • Giese, B., and D. Jay, 1989: Modelling tidal energetics of the Columbia River estuary. Estuarine Coastal Shelf Sci., 29, 549571, doi:10.1016/0272-7714(89)90010-3.

    • Search Google Scholar
    • Export Citation
  • Hansen, D. V., and M. Rattray Jr., 1965: Gravitational circulation in straits and estuaries. J. Mar. Res., 23, 104122.

  • Hughes, F., and M. Rattray Jr., 1980: Salt flux and mixing in the Columbia River estuary. Estuarine Coastal Mar. Sci., 10, 479493, doi:10.1016/S0302-3524(80)80070-3.

    • Search Google Scholar
    • Export Citation
  • Ianniello, J. P., 1979: Tidally induced residual currents in estuaries of variable breadth and depth. J. Phys. Oceanogr., 9, 962974, doi:10.1175/1520-0485(1979)009<0962:TIRCIE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Smith, 1990a: Residual circulation in shallow estuaries: 1. Highly stratified, narrow estuaries. J. Geophys. Res., 95, 711731, doi:10.1029/JC095iC01p00711.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Smith, 1990b: Residual circulation in shallow estuaries: 2. Weakly stratified and partially mixed systems. J. Geophys. Res., 95, 733748, doi:10.1029/JC095iC01p00733.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Smith, 1990c: Circulation, density distribution and neap-spring transitions in the Columbia River estuary. Prog. Oceanogr., 25, 81112, doi:10.1016/0079-6611(90)90004-L.

    • Search Google Scholar
    • Export Citation
  • Jones, J., and A. Davies, 1996: A high-resolution, three-dimensional model of the M2, M4, M6, S2, N2, K1 and O1 tides in the eastern Irish Sea. Estuarine Coastal Shelf Sci., 42, 311346, doi:10.1006/ecss.1996.0022.

    • Search Google Scholar
    • Export Citation
  • Kjerfve, B., 1986: Circulation and salt flux in a well mixed estuary. Physics of Shallow Estuaries and Bays, J. van de Kreeke, Ed., Lecture Notes on Coastal and Estuarine Studies Series, Vol. 16, Amer. Geophys. Union, 22–29.

  • Kuijper, K., and L. C. Van Rijn, 2011: Analytical and numerical analysis of tides and salinities in estuaries; Part II: Salinity distributions in prismatic and convergent tidal channels. Ocean Dyn., 61, 17431765, doi:10.1007/s10236-011-0454-z.

    • Search Google Scholar
    • Export Citation
  • Lanzoni, S., and G. Seminara, 1998: On tide propagation in convergent estuaries. J. Geophys. Res., 103, 30 79330 812, doi:10.1029/1998JC900015.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., W. R. Geyer, and R. J. Chant, 2006: Mechanisms driving the time-dependent salt flux in a partially stratified estuary. J. Phys. Oceanogr., 36, 22962311, doi:10.1175/JPO2959.1.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., 2004: Toward a unified theory of tidally-averaged estuarine salinity structure. Estuaries, 27, 561570, doi:10.1007/BF02907644.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., and W. R. Geyer, 2010: Advances in estuarine physics. Annu. Rev. Mar. Sci., 2, 3558, doi:10.1146/annurev-marine-120308-081015.

    • Search Google Scholar
    • Export Citation
  • McCarthy, R. K., 1993: Residual currents in tidally dominated, well-mixed estuaries. Tellus, 45A, 325340, doi:10.1034/j.1600-0870.1993.00007.x.

    • Search Google Scholar
    • Export Citation
  • Peters, J., and R. Wollast, 1976: Role of the sedimentation in the self-purification of the Scheldt estuary. Proc. Third Federal Interagency Sedimentation Conf., Denver, CO, Water Resources Council, 3-77–3-82.

  • Prandle, D., 2003: Relationships between tidal dynamics and bathymetry in strongly convergent estuaries. J. Phys. Oceanogr., 33, 27382750, doi:10.1175/1520-0485(2003)033<2738:RBTDAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rattray, M., and J. Dworski, 1980: Comparison of methods for analysis of the transverse and vertical circulation contributions to the longitudinal advective salt flux in estuaries. Estuarine Coastal Mar. Sci., 11, 515536, doi:10.1016/S0302-3524(80)80004-1.

    • Search Google Scholar
    • Export Citation
  • Savenije, H. H., 1993: Composition and driving mechanisms of longitudinal tidal average salinity dispersion in estuaries. J. Hydrol., 144, 127141, doi:10.1016/0022-1694(93)90168-9.

    • Search Google Scholar
    • Export Citation
  • Savenije, H. H., 2012: Salinity and Tides in Alluvial Estuaries. 2nd ed. Savenije, 163 pp. [Available online at https://salinityandtides.com/.]

  • Savenije, H. H., and E. J. Veling, 2005: Relation between tidal damping and wave celerity in estuaries. J. Geophys. Res., 110, C04007, doi:10.1029/2004JC002278.

    • Search Google Scholar
    • Export Citation
  • Schramkowski, G. P., and H. de Swart, 2002: Morphodynamic equilibrium in straight tidal channels: Combined effects of Coriolis force and external overtides. J. Geophys. Res., 107, 3227, doi:10.1029/2000JC000693.

    • Search Google Scholar
    • Export Citation
  • Schramkowski, G. P., H. de Swart, and H. M. Schuttelaars, 2010: Effect of bottom stress formulation on modelled flow and turbidity maxima in cross-sections of tide-dominated estuaries. Ocean Dyn., 60, 205218, doi:10.1007/s10236-009-0235-0.

    • Search Google Scholar
    • Export Citation
  • Souza, A., 2013: On the use of the Stokes number to explain frictional tidal dynamics and water column structure in shelf seas. Ocean Sci., 9, 391398, doi:10.5194/os-9-391-2013.

    • Search Google Scholar
    • Export Citation
  • Taylor, G., 1953: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Roy. Soc. London, A219, 186203, doi:10.1098/rspa.1953.0139.

    • Search Google Scholar
    • Export Citation
  • Taylor, G., 1954: The dispersion of matter in turbulent flow through a pipe. Proc. Roy. Soc. London, A223, 446468, doi:10.1098/rspa.1954.0130.

    • Search Google Scholar
    • Export Citation
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