• Agnew, R., 1960: Estuarine currents and tidal streams. Coastal Eng. Proc.,7, 510–535.

  • Banas, N. S., and B. M. Hickey, 2005: Mapping exchange and residence time in a model of Willapa Bay, Washington, a branching, macrotidal estuary. J. Geophys. Res.,110, C11011, doi:10.1029/2005JC002950.

  • Becherer, J., and L. Umlauf, 2011: Boundary mixing in lakes: 1. Modeling the effect of shear-induced convection. J. Geophys. Res.,116, C10017, doi:10.1029/2011JC007119.

  • Becherer, J., H. Burchard, G. Flöser, V. Mohrholz, and L. Umlauf, 2011: Evidence of tidal straining in well-mixed channel flow from microstructure observations. Geophys. Res. Lett.,38, L17611, doi:10.1029/2011GL049005.

  • Becherer, J., M. T. Stacey, L. Umlauf, and H. Burchard, 2015: Lateral circulation generates flood-tide stratification and estuarine exchange flow in a curved tidal inlet. J. Phys. Oceanogr., 45, 638656, doi:10.1175/JPO-D-14-0001.1.

    • Search Google Scholar
    • Export Citation
  • Buckingham, E., 1914: On physically similar systems; Illustrations of the use of dimensional equations. Phys. Rev., 4, 345376, doi:10.1103/PhysRev.4.345.

    • Search Google Scholar
    • Export Citation
  • Buijsman, M., and H. Ridderinkhof, 2008: Variability of secondary currents in a weakly stratified tidal inlet with low curvature. Cont. Shelf Res., 28, 17111723, doi:10.1016/j.csr.2008.04.001.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., and R. Hofmeister, 2008: A dynamic equation for the potential energy anomaly for analysing mixing and stratification in estuaries and coastal seas. Estuarine Coastal Shelf Sci., 77, 679687, doi:10.1016/j.ecss.2007.10.025.

    • 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., and H. M. Schuttelaars, 2012: Analysis of tidal straining as driver for estuarine circulation in well-mixed estuaries. J. Phys. Oceanogr., 42, 261271, doi:10.1175/JPO-D-11-0110.1.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., G. Flöser, J. V. Staneva, T. H. Badewien, and R. Riethmüller, 2008: Impact of density gradients on net sediment transport into the Wadden Sea. J. Phys. Oceanogr., 38, 566587, doi:10.1175/2007JPO3796.1.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., F. Janssen, K. Bolding, L. Umlauf, and H. Rennau, 2009: Model simulations of dense bottom currents in the western Baltic Sea. Cont. Shelf Res., 29, 205220, doi:10.1016/j.csr.2007.09.010.

    • 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
  • Burchard, H., H. M. Schuttelaars, and W. R. Geyer, 2013: Residual sediment fluxes in weakly-to-periodically stratified estuaries and tidal inlets. J. Phys. Oceanogr., 43, 18411861, doi:10.1175/JPO-D-12-0231.1.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., E. Schulz, and H. M. Schuttelaars, 2014: Impact of estuarine convergence on residual circulation in tidally energetic estuaries and inlets. Geophys. Res. Lett., 41, 913919, doi:10.1002/2013GL058494.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., 2002: Secondary circulation in a region of flow curvature: Relationship with tidal forcing and river discharge. J. Geophys. Res.,107, 3131, doi:10.1029/2001JC001082.

  • de Boer, G. J., J. D. Pietrzak, and J. C. Winterwerp, 2008: Using the potential energy anomaly equation to investigate tidal straining and advection of stratification in a region of freshwater influence. Ocean Modell., 22, 111, doi:10.1016/j.ocemod.2007.12.003.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., 1993: Three-dimensional tidal flow around headlands. J. Geophys. Res., 98, 955966, doi:10.1029/92JC02270.

  • Geyer, W. R., and J. D. Smith, 1987: Shear instability in a highly stratified estuary. J. Phys. Oceanogr., 17, 16681679, doi:10.1175/1520-0485(1987)017<1668:SIIAHS>2.0.CO;2.

    • 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
  • Giddings, S. N., D. A. Fong, and S. G. Monismith, 2011: Role of straining and advection in the intratidal evolution of stratification, vertical mixing, and longitudinal dispersion of a shallow, macrotidal, salt wedge estuary. J. Geophys. Res.,116, C03003, doi:10.1029/2010JC006482.

  • Giddings, S. N., and Coauthors, 2012: Frontogenesis and frontal progression of a trapping-generated estuarine convergence front and its influence on mixing and stratification. Estuaries Coasts, 35, 665681, doi:10.1007/s12237-011-9453-z.

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

  • Howlett, E. R., T. P. Rippeth, and J. Howarth, 2011: Processes contributing to the evolution and destruction of stratification in the Liverpool Bay ROFI. Ocean Dyn., 61, 14031419, doi:10.1007/s10236-011-0402-y.

    • Search Google Scholar
    • Export Citation
  • Huijts, K. M., H. E. de Swart, G. P. Schramkowski, and H. M. Schuttelaars, 2011: Transverse structure of tidal and residual flow and sediment concentration in estuaries. Ocean Dyn., 61, 10671091, doi:10.1007/s10236-011-0414-7.

    • 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. Musiak, 1994: Particle trapping in estuarine tidal flows. J. Geophys. Res., 99, 20 44520 461, doi:10.1029/94JC00971.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Musiak, 1996: Internal tidal asymmetry in channel flows: origins and consequences. Mixing in Estuaries and Coastal Seas, C. Pattiaratchi, Ed., Coastal and Estuarine Studies, Vol. 50, Amer. Geophys. Union, 211–249.

  • Kalagnanam, J., M. Henrion, and E. Subrahmanian, 1994: The scope of dimensional analysis in qualitative reasoning. Comput. Intell., 10, 117133, doi:10.1111/j.1467-8640.1994.tb00160.x.

    • Search Google Scholar
    • Export Citation
  • Kundu, P. K., and I. M. Cohen, 2002: Fluid Mechanics. 2nd ed. Academic Press, 730 pp.

  • Lacy, J. R., M. T. Stacey, J. R. Burau, and S. G. Monismith, 2003: Interaction of lateral baroclinic forcing and turbulence in an estuary. J. Geophys. Res., 108, 3089, doi:10.1029/2002JC001392.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., and W. R. Geyer, 2004: Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr., 34, 14101428, doi:10.1175/1520-0485(2004)034<1410:MTLCIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Linden, P. F., 1979: Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn., 13, 323, doi:10.1080/03091927908243758.

  • Linden, P. F., 1980: Mixing across a density interface produced by grid turbulence. J. Fluid Mech., 100, 691703, doi:10.1017/S002211208000136X.

    • Search Google Scholar
    • Export Citation
  • Linden, P. F., and J. E. Simpson, 1986: Gravity-driven flows in a turbulent fluid. J. Fluid Mech., 172, 481497, doi:10.1017/S0022112086001829.

    • Search Google Scholar
    • Export Citation
  • Linden, P. F., and J. E. Simpson, 1988: Modulated mixing and frontogenesis in shallow seas and estuaries. Cont. Shelf Res., 8, 11071127, doi:10.1016/0278-4343(88)90015-5.

    • 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
  • Nunes, R. A., and J. H. Simpson, 1985: Axial convergence in a well-mixed estuary. Estuarine Coastal Shelf Sci., 20, 637649, doi:10.1016/0272-7714(85)90112-X.

    • Search Google Scholar
    • Export Citation
  • Peters, H., 1997: Observations of stratified turbulent mixing in an estuary: Neap-to-spring variations during high river flow. Estuarine Coastal Shelf Sci.,45, 69–88, doi:10.1006/ecss.1996.0180.

  • Pritchard, D. W., 1952: Salinity distribution and circulation in the Chesapeake Bay estuarine system. J. Mar. Res., 11, 106123.

  • Purkiani, K., J. Becherer, G. Flöser, U. Gräwe, V. Mohrholz, H. M. Schuttelaars, and H. Burchard, 2015: Numerical analysis of stratification and destratification processes in a tidally energetic inlet with an ebb tidal delta. J. Geophys. Res. Oceans, 120, 225243, doi:10.1002/2014JC010325.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., and C. T. Friedrichs, 2007: The importance of tidal and lateral asymmetries in stratification to residual circulation in partially mixed estuaries. J. Phys. Oceanogr., 37, 14961511, doi:10.1175/JPO3071.1.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., and W. R. Geyer, 2012: The role of advection, straining, and mixing on the tidal variability of estuarine stratification. J. Phys. Oceanogr., 42, 855868, doi:10.1175/JPO-D-10-05010.1.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., C. Friedrichs, and J. Brubaker, 2005: Control of estuarine stratification and mixing by wind-induced straining of the estuarine density field. Estuaries, 28, 321326, doi:10.1007/BF02693915.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., W. R. Geyer, and J. A. Lerczak, 2009: The influence of lateral advection on the residual estuarine circulation: A numerical modeling study of the Hudson River estuary. J. Phys. Oceanogr., 39, 107124, doi:10.1175/2008JPO3952.1.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., D. J. Crisp, and C. Hearn, 1981: The shelf-sea fronts: Implications of their existence and behaviour. Philos. Trans. Roy. Soc. London, A302, 531546, doi:10.1098/rsta.1981.0181.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., J. Brown, J. Matthews, and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13, 125132, doi:10.2307/1351581.

    • Search Google Scholar
    • Export Citation
  • Smith, R., 1976: Longitudinal dispersion of a buoyant contaminant in a shallow channel. J. Fluid Mech., 78, 677688, doi:10.1017/S0022112076002681.

    • Search Google Scholar
    • Export Citation
  • Souza, A. J., 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
  • Stacey, M. T., S. G. Monismith, and J. R. Burau, 1999: Observations of turbulence in a partially stratified estuary. J. Phys. Oceanogr., 29, 19501970, doi:10.1175/1520-0485(1999)029<1950:OOTIAP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Stacey, M. T., J. R. Burau, and S. G. Monismith, 2001: Creation of residual flows in a partially stratified estuary. J. Geophys. Res., 106, 17 01317 037, doi:10.1029/2000JC000576.

    • Search Google Scholar
    • Export Citation
  • Valle-Levinson, A., 2008: Density-driven exchange flow in terms of the Kelvin and Ekman numbers. J. Geophys. Res.,113, C04001, doi:10.1029/2007JC004144.

  • Valle-Levinson, A., C. Li, K.-C. Wong, and K. M. M. Lwiza, 2000: Convergence of lateral flow along a coastal plain estuary. J. Geophys. Res., 105, 17 04517 061, doi:10.1029/2000JC900025.

    • Search Google Scholar
    • Export Citation
  • van Rijn, L. C., 2011: Analytical and numerical analysis of tides and salinities in estuaries; Part I: Tidal wave propagation in convergent estuaries. Ocean Dyn., 61, 17191741, doi:10.1007/s10236-011-0453-0.

    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., and A. Valle-Levinson, 2010: Transverse structure of subtidal flow in a weakly stratified subtropical tidal inlet. Cont. Shelf Res., 30, 281292, doi:10.1016/j.csr.2009.11.008.

    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., B. Tutak, A. Valle-Levinson, and Y. P. Sheng, 2013: Influence of two tropical storms on the residual flow in a subtropical tidal inlet. Estuaries Coasts, 36, 10371053, doi:10.1007/s12237-013-9606-3.

    • Search Google Scholar
    • Export Citation
  • Winant, C. D., 2008: Three-dimensional residual tidal circulation in an elongated, rotating basin. J. Phys. Oceanogr., 38, 1278–1295, doi:10.1175/2007JPO3819.1.

    • Search Google Scholar
    • Export Citation
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Impact of the Depth-to-Width Ratio of Periodically Stratified Tidal Channels on the Estuarine Circulation

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  • 1 Leibniz Institute for Baltic Sea Research Warnemünde, Rostock, Germany
  • | 2 Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands
  • | 3 Leibniz Institute for Baltic Sea Research Warnemünde, Rostock, Germany
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Abstract

The dependency of the estuarine circulation on the depth-to-width ratio of a periodically, weakly stratified tidal estuary is systematically investigated here for the first time. Currents, salinity, and other properties are simulated by means of the General Estuarine Transport Model (GETM) in cross-sectional slice mode, applying a symmetric Gaussian-shaped depth profile. The width is varied over four orders of magnitude. The individual along-channel circulation contributions from tidal straining, gravitation, advection, etc., are calculated and the impact of the depth-to-width ratio on their intensity is presented and elucidated. It is found that the estuarine circulation exhibits a distinct maximum in medium-wide channels (intermediate depth-to-width ratio depending on various parameters), which is caused by a maximum of the tidal straining contribution. This maximum is related to a strong tidal asymmetry of eddy viscosity and shear created by secondary strain-induced periodic stratification (2SIPS): in medium channels, transverse circulation generated by lateral density gradients due to laterally differential longitudinal advection induces stable stratification at the end of the flood phase, which is further increased during ebb by longitudinal straining (SIPS). Thus, eddy viscosity is low and shear is strong in the entire ebb phase. During flood, SIPS decreases the stratification so that eddy viscosity is high and shear is weak. The circulation resulting from this viscosity–shear correlation, the tidal straining circulation, is oriented like the classical, gravitational circulation, with riverine outflow at the surface and oceanic inflow close to the bottom. In medium channels, it is about 5 times as strong as in wide (quasi one-dimensional) channels, in which 2SIPS is negligible.

Corresponding author address: Elisabeth Schulz, Leibniz Institute for Baltic Sea Research Warnemünde, Seestrasse 15, 18119 Rostock, Germany. E-mail: e.schulz.fischer@gmail.com

Abstract

The dependency of the estuarine circulation on the depth-to-width ratio of a periodically, weakly stratified tidal estuary is systematically investigated here for the first time. Currents, salinity, and other properties are simulated by means of the General Estuarine Transport Model (GETM) in cross-sectional slice mode, applying a symmetric Gaussian-shaped depth profile. The width is varied over four orders of magnitude. The individual along-channel circulation contributions from tidal straining, gravitation, advection, etc., are calculated and the impact of the depth-to-width ratio on their intensity is presented and elucidated. It is found that the estuarine circulation exhibits a distinct maximum in medium-wide channels (intermediate depth-to-width ratio depending on various parameters), which is caused by a maximum of the tidal straining contribution. This maximum is related to a strong tidal asymmetry of eddy viscosity and shear created by secondary strain-induced periodic stratification (2SIPS): in medium channels, transverse circulation generated by lateral density gradients due to laterally differential longitudinal advection induces stable stratification at the end of the flood phase, which is further increased during ebb by longitudinal straining (SIPS). Thus, eddy viscosity is low and shear is strong in the entire ebb phase. During flood, SIPS decreases the stratification so that eddy viscosity is high and shear is weak. The circulation resulting from this viscosity–shear correlation, the tidal straining circulation, is oriented like the classical, gravitational circulation, with riverine outflow at the surface and oceanic inflow close to the bottom. In medium channels, it is about 5 times as strong as in wide (quasi one-dimensional) channels, in which 2SIPS is negligible.

Corresponding author address: Elisabeth Schulz, Leibniz Institute for Baltic Sea Research Warnemünde, Seestrasse 15, 18119 Rostock, Germany. E-mail: e.schulz.fischer@gmail.com
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