• Adams Jr.,, C. E., and G. L. Weatherly, 1981: Some effects of suspended sediment stratification on an oceanic bottom boundary layer. J. Geophys. Res., 86 , 41614172.

    • Search Google Scholar
    • Export Citation
  • Anwar, H. O., 1983: Turbulence measurements in stratified and well-mixed estuarine flows. Estuarine Coastal Shelf Sci., 17 , 243260.

  • Ariathurai, R., and R. B. Krone, 1976: Mathematical modelling of sediment transport in estuaries. Circulation, Sediments, and Transfer of Material in the Estuary, M. Wiley, Ed., Estuarine Processes, Vol. II, Academic Press, 98–106.

    • Search Google Scholar
    • Export Citation
  • Armi, L., and E. D'Asaro, 1980: Flow structures of the benthic ocean. J. Geophys. Res., 85 , 469484.

  • Blumberg, A. F., and G. L. Mellor, 1983: Diagnostic and prognostic numerical circulation studies of the South Atlantic Bight. J. Geophys. Res., 88 , 45794592.

    • Search Google Scholar
    • Export Citation
  • Blumberg, A. F., and G. L. Mellor, 1987: A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Models of Marine and Estuarine Dynamics, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier Oceanography Series, Vol. 45, Elsevier, 55–88.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28 , 181189.

    • Search Google Scholar
    • Export Citation
  • Chao, S-Y., 1998: Hyperpycnal and buoyant plumes from a sediment-laden river. J. Geophys. Res., 103 , 30673082.

  • Cheng, R., C-H. Ling, J. W. Gartner, and P. F. Wang, 1999: Estimates of bottom roughness length and bottom shear stress in south San Francisco Bay, California. J. Geophys. Res., 104 , 77157728.

    • Search Google Scholar
    • Export Citation
  • Clark, S., and A. J. Elliot, 1998: Modelling suspended sediment concentration in the Firth of Forth. Estuarine Coastal Shelf Sci., 47 , 235250.

    • Search Google Scholar
    • Export Citation
  • Dickey, T. D., and M. L. Mellor, 1980: Decaying turbulence in neutral and stratified fluids. J. Fluid Mech., 99 , 1331.

  • Ezer, T., 2000: On the seasonal mixed layer simulated by a basin-scale ocean model and the Mellor–Yamada turbulence scheme. J. Geophys. Res., 105 , 1684316855.

    • Search Google Scholar
    • Export Citation
  • Fohrmann, H., J. O. Backhaus, F. Laume, and J. Rumohr, 1998: Sediments in bottom-arrested gravity plumes: Numerical case studies. J. Phys. Oceanogr., 28 , 22502274.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., 1993: The importance of suppression of turbulence by stratification on the estuarine turbidity maximum. Estuaries, 16 , 113125.

    • Search Google Scholar
    • Export Citation
  • Gibbs, R. J., and L. Konwar, 1986: Congulation and settling of Amazon River suspended sediment. Cont. Shelf Res., 6 , 127149.

  • Glenn, S. M., and W. D. Grant, 1987: A suspended sediment stratification correction for combined wave and current flows. J. Geophys. Res., 92 , 82448264.

    • Search Google Scholar
    • Export Citation
  • Kampf, J., J. O. Backhaus, and H. Fohrmann, 1999: Sediment-induced slope convection: Two-dimensional numerical case studies. J. Geophys. Res., 104 , 2050920522.

    • Search Google Scholar
    • Export Citation
  • King, B., and E. Wolanski, 1996: Bottom friction reduction in turbid estuaries. Mixing in Estuaries and Coastal Studies, C. Pattiaratchi, Ed., Amer. Geophys. Union, 325–337.

    • Search Google Scholar
    • Export Citation
  • Lyne, V. D., B. Butman, and W. D. Grant, 1990a: Sediment movement along the U.S. East Coast continental shelf—I. Estimates of bottom stress using the Grant–Madsen model and near bottom wave and currents measurements. Cont. Shelf Res., 10 , 397428.

    • Search Google Scholar
    • Export Citation
  • Lyne, V. D., B. Butman, and W. D. Grant, 1990b: Sediment movement along the U.S. East Coast continental shelf—II. Modelling suspended sediment concentration and transport rate during storms. Cont. Shelf Res., 10 , 429460.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., and P. B. Rhines, 1993: Slippery bottom boundary layers on a slope. J. Phys. Oceanogr., 23 , 522.

  • Martin, P. J., 1985: Simulation of the mixed layer at OWS November and Papa with several models. J. Geophys. Res., 90 , 903916.

  • Mehta, A. J., 1984: Characterization of cohesive sediment properties and transport progresses in estuaries. Estuarine Cohesive Sediment Dynamics, A. J. Mehta, Ed., Springer-Verlag, 468 pp.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 1998: User's guide for a three-dimensional, primitive equation numerical ocean model. Princeton University Rep., 41 pp. [Available from Program in Atmospheric and Oceanic Science, Princeton University, Princeton, NJ 08544.].

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2001: One-dimensional, ocean surface layer modeling: A problem and a solution. J. Phys. Oceanogr., 31 , 790809.

  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31 , 17911806.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20 , 851875.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and X. H. Wang, 1996: Pressure compensation and the bottom boundary layer. J. Phys. Oceanogr., 26 , 22142222.

  • Oey, L-Y., G. L. Mellor, and R. I. Hires, 1985a: A three-dimensional simulation of the Hudson–Raritan estuary. Part I: Description of the model and model simulations. J. Phys. Oceanogr., 15 , 16761692.

    • Search Google Scholar
    • Export Citation
  • Oey, L-Y., G. L. Mellor, and R. I. Hires, 1985b: A three-dimensional simulation of the Hudson–Raritan estuary. Part II: Comparison with observation. J. Phys. Oceanogr., 15 , 16931709.

    • Search Google Scholar
    • Export Citation
  • Sangiorgi, F., R. Setti, G. Gabbianelli, and C. Trombini, 1998: Geochemical characterisation of Hg-contaminated sediments of the “Pialassa Baiona” (Ravenna Lagoon, Italy). Rapp. Comm. Int. Explor. Sci. Mer Mediterr., 35 , 9697.

    • Search Google Scholar
    • Export Citation
  • Sheng, Y. P., 1984: Modelling bottom boundary layer and cohesive sediment dynamics in estuarine and coastal waters. Estuarine Cohesive Sediment Dynamics, A. J. Mehta, Ed., Springer-Verlag, 360–400.

    • Search Google Scholar
    • Export Citation
  • Smith, J. D., and S. R. McLean, 1977: Spatially averaged flow over a wavy surface. J. Geophys. Res., 82 , 17351746.

  • Smolarkiewicz, P. K., 1984: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comput. Phys., 54 , 325362.

    • Search Google Scholar
    • Export Citation
  • Soulsby, R. L., and B. L. S. A. Wainwright, 1987: A criterion for the effect of suspended sediment on near-bottom velocity profiles. J. Hydraul. Res., 25 , 341356.

    • Search Google Scholar
    • Export Citation
  • Taylor, P. A., and K. R. Dyer, 1977: Theoretical models of flow near the bed and their implications for sediment transport. The Sea, E. D. Goldberg, Ed., Vol. 6, Marine Modeling, Wiley and Sons, 579–601.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., and S. J. Lentz, 1991: Asymmetric behavior of the oceanic boundary layer above a sloping bottom. J. Phys. Oceanogr., 21 , 11711185.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., and G. C. Kineke, 1994: Structure and dynamics of fluid muds over the Amazon continental shelf. J. Geophys. Res., 99 , 865874.

    • Search Google Scholar
    • Export Citation
  • van Rijn, L. C., 1984: Sediment transport. Part II: Suspended load transport. J. Hydraul. Eng., ASCE, 110 , 16131641.

  • Wang, X. H., 2001: A numerical study of sediment transport in a coastal embayment during winter storms. J. Coastal Res., 34 (Special Issue) 414427.

    • Search Google Scholar
    • Export Citation
  • Wang, X. H., and P. D. Craig, 1993: An analytic model of tidal circulation in a narrow estuary. J. Mar. Res., 51 , 447465.

  • Weatherly, G. L., and P. J. Martin, 1978: On the structure and dynamics of the oceanic bottom boundary layer. J. Phys. Oceanogr., 8 , 557570.

    • Search Google Scholar
    • Export Citation
  • Wright, L. D., W. J. Wiseman Jr.,, Z-S. Yang, B. D. Bornhold, G. H. Keller, D. B. Prior, and J. N. Suhayda, 1990: Processes of marine dispersal and deposition of suspended silts off the modern mouth of the Huanghe (Yellow River). Cont. Shelf Res., 10 , 140.

    • Search Google Scholar
    • Export Citation
  • Zavatarelli, M., and G. L. Mellor, 1995: A numerical study of the Mediterranean Sea circulation. J. Phys. Oceanogr., 25 , 13841414.

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    Schematic explanation of basic terms and the model domain of an idealized estuary

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    Time series of the tidal elevation and the total sediment transport across the section at x = 30 km, predicted by expt 1a (thin line) and expt 1b (thick line)

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    Sediment concentration C and horizontal flux Q for spring flood tide (t = 25 days) along an axial cross section in the estuary. The actual model domain extends 10 km farther downstream. The cross-estuary variations in C and Q predicted by the model are negligible. (a) Model prediction from expt 1a and (b) model prediction from expt 1b. The negative flux indicates an upstream sediment transport by the flood tide

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    As in Fig. 2 but for the flux Richardson number Rf and friction velocity u∗. A five-point Laplacian spatial filter is applied to both Rf and u∗ in order to remove smaller-scale noise

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    Vertical and temporal variation of sediment concentration C and the horizontal flux Q at x = 30 km, predicted by (a) expt 1a and (b) expt 1b for the second spring–neap tidal cycle. Positive Q indicates sediment transport downstream and is denoted by the solid lines

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    Vertical and temporal variation of sediment concentration C and the horizontal flux Q at x = 30 km from day 22 to 26, predicted by expt 1b. Positive Q indicates sediment transport downstream and is denoted by the solid lines

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    Vertical and temporal variation of the flux Richardson number Rf and friction velocity u∗ at x = 30 km from day 22 to 26, predicted by expt 1b

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    As in Fig. 7 but for (a) x = 25 km and (b) x = 40 km.

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    As in Fig. 7 but predicted by (a) expt 2a, (b) expt 2b, and (c) expt 1a.

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    (Continued)

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    Sediment distribution in the water column for the period from day 22 to 26. The sediment concentration was predicted by expt 1b at (a) x = 25 km, (b) x = 30 km, (c) x = 40 km; (d) expt 2a at x = 30 km; (e) expt 2b at x = 30 km; (f) expt 1b with corrected M–Y turbulence scheme at x = 30 km; and (g) expt 1b with the effect of sediment particle flocculation at x = 30 km

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    The flux Richardson number Rf for spring flood tide (t = 25 days) along an axial cross section in the estuary predicted by (a) expt 3a and (b) expt 3b. A five-point Laplacian spatial filter is applied to both Rf and u

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    Spring–tidal mean sediment concentration C and cross-estuary velocity υ along an axial cross-section in the estuary; C and υ are averaged over 10 days (5 days before and after the spring tide). (a) Model prediction from expt 1b, (b) model prediction from expt 4a, and (c) model prediction from expt 4b. Negative velocity indicates a current flowing out of the page.

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    As in Fig. 12 but for expt 5. (a) Model prediction from expt 5a, (b) model prediction from expt 5b, and (c) model prediction from expt 5c.

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    The effect of sediment stratification and the model vertical resolution on the bottom drag coefficient Cd

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    Time series of the tidal mean bottom drag coefficient at x = 30 km, predicted by expt 1a (thin line) and expt 1b (thick line)

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Tide-Induced Sediment Resuspension and the Bottom Boundary Layer in an Idealized Estuary with a Muddy Bed

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  • 1 School of Geography and Oceanography, University of New South Wales, Australian Defence Force Academy, Canberra, Australia
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Abstract

Sediment transport and bottom boundary layer (BBL) in an idealized estuary with a muddy bed were studied by numerical simulations. The focus was placed on description and prediction of the dynamics of nepheloid layer (a fluid–mud layer) developed in the estuary because of the coupling effect of the seawater and resuspended sediment concentration. The Princeton Ocean Model was coupled to a sediment transport model to conduct the numerical experiments. A semidiurnal tide with a spring–neap cycle was used to force the model at the estuary entrance. A stability function was introduced to the bottom drag coefficient Cd for a slip bottom boundary condition in order to consider the effects of sediment-induced stratification. When the seawater density is not affected by the resuspended sediments, spring tides resuspend sediments to the sea surface near the estuary entrance where the bottom stress is larger than the critical stress value. The sediment distribution in the BBL near the entrance is dominantly affected by the vertical eddy diffusion, and the time series of the sediment concentration presents two high value peaks within a tidal cycle. Above the BBL the sediment concentration is primarily controlled by the horizontal tidal advection; thus a semidiurnal oscillation in sediment concentration is predicted. When the seawater density and the sediment concentration are coupled, the sediments resuspended by the spring tides are only distributed in the bottom layer with a thickness of a few meters. A lutocline is developed above a nepheloid layer where the vertical sediment concentration gradient is of maximum. The settlement of the nepheloid layer gives rise to the resuspension events that are characterized with an abnormally high value in sediment concentration within a thin wall layer that is overlaid by a thicker layer with much smaller concentration. This two-layer sediment distribution structure was observed on the continental shelf off the mouth of the Amazon River. These resuspension events may be referred to as “resuspension hysteresis” with respect to the tidal forcing frequency. The frequency of the resuspension hysteresis is controlled by both the sediment settling velocity and the turbulence intensity, and is lower than that of the tidal forcing. A hyperpycnal plume is also established near the entrance, generating a cross-estuary tidal mean flow on the order of 1 cm s−1 there. Variability in Cd between the spring and neap tides is predicted because of the sediment-induced stratification, and the prediction agrees, in general term, with observations in south San Francisco Bay.

Corresponding author address: Dr. X. H. Wang, University College, University of New South Wales, ADFA, Canberra, ACT 2600, Australia. Email: hua.wang@adfa.edu.au

Abstract

Sediment transport and bottom boundary layer (BBL) in an idealized estuary with a muddy bed were studied by numerical simulations. The focus was placed on description and prediction of the dynamics of nepheloid layer (a fluid–mud layer) developed in the estuary because of the coupling effect of the seawater and resuspended sediment concentration. The Princeton Ocean Model was coupled to a sediment transport model to conduct the numerical experiments. A semidiurnal tide with a spring–neap cycle was used to force the model at the estuary entrance. A stability function was introduced to the bottom drag coefficient Cd for a slip bottom boundary condition in order to consider the effects of sediment-induced stratification. When the seawater density is not affected by the resuspended sediments, spring tides resuspend sediments to the sea surface near the estuary entrance where the bottom stress is larger than the critical stress value. The sediment distribution in the BBL near the entrance is dominantly affected by the vertical eddy diffusion, and the time series of the sediment concentration presents two high value peaks within a tidal cycle. Above the BBL the sediment concentration is primarily controlled by the horizontal tidal advection; thus a semidiurnal oscillation in sediment concentration is predicted. When the seawater density and the sediment concentration are coupled, the sediments resuspended by the spring tides are only distributed in the bottom layer with a thickness of a few meters. A lutocline is developed above a nepheloid layer where the vertical sediment concentration gradient is of maximum. The settlement of the nepheloid layer gives rise to the resuspension events that are characterized with an abnormally high value in sediment concentration within a thin wall layer that is overlaid by a thicker layer with much smaller concentration. This two-layer sediment distribution structure was observed on the continental shelf off the mouth of the Amazon River. These resuspension events may be referred to as “resuspension hysteresis” with respect to the tidal forcing frequency. The frequency of the resuspension hysteresis is controlled by both the sediment settling velocity and the turbulence intensity, and is lower than that of the tidal forcing. A hyperpycnal plume is also established near the entrance, generating a cross-estuary tidal mean flow on the order of 1 cm s−1 there. Variability in Cd between the spring and neap tides is predicted because of the sediment-induced stratification, and the prediction agrees, in general term, with observations in south San Francisco Bay.

Corresponding author address: Dr. X. H. Wang, University College, University of New South Wales, ADFA, Canberra, ACT 2600, Australia. Email: hua.wang@adfa.edu.au

1. Introduction

Bottom boundary layers (BBL) play an important role in water circulation in the open oceans (Mellor and Wang 1996) and, according to Zavatarelli and Mellor (1995), Oey et al. (1985a,b), and Wang and Craig (1993), in shallow seas and estuaries as well. Hydrodynamic properties such as current shear stress and turbulent eddy diffusivity in the BBL directly control sediment resuspension and transport in estuaries and continental shelves (e.g., Ariathurai and Krone 1976, Lyne et al. 1990a,b; Burchard and Baumert 1998; Cheng et al. 1999). Bottom boundary layers are the regions where vigorous turbulent mixing are taking place due to the presence of strong current shear (Mellor and Yamada 1974; Armi and D'Asaro 1980). Nevertheless, the waters in the BBLs may be stratified by stable thermal structures (Weatherly and Martin 1978) or by the sediments resuspended from the seabed (e.g., Smith and McLean 1977; Adams and Weatherly 1981; van Rijn 1984; Soulsby and Wainwright 1987; Glenn and Grant 1987; Geyer 1993). Hydrodynamic characteristics of the stratified BBLs are significantly different to those in well-mixed BBLs as the turbulence is damped by the stratification, and the bottom friction is significantly reduced (King and Wolanski 1996). On a slope bottom, bottom boundary Ekman transport can change the density field of the overlying water and causes a “shutdown” of the boundary layer (Trowbridge and Lenz 1991; MacCready and Rhines 1993).

In tidal estuaries, riverborne, clay-rich sediments derived from erosion of the catchment basin encounters the higher salinity of seawater and often aggregates into larger particles. that settle to form mudflats and saltmarshes. The clay-rich sediment particles are electrically charged and therefore become agents capable of attracting pollutants such as heavy metals and nutrients. Tidal currents resuspend newly deposited sediments and resuspended sediment concentration can reach as high as 1 g L−1 (e.g., in the Yellow River and the Amazon River: Wright et al. 1990; Gibbs and Konwar 1986). Sediment contribution to the water density with above concentration value is equivalent to a salinity increase of 0.76 psu (Fohrmann et al. 1998). A nepheloid layer (a fluid–mud layer) is often developed above the seabed and stratifies the BBL. The development of the nepheloid layer inhibits an upward vertical transport of the nutrients as well as the pollutants trapped beneath it (Sangiorgi et al. 1998). Therefore, an understanding of the dynamics of nepheloid layers is urgently needed to study biogeochemical processes in a turbid ecosystem environment.

This paper studies tide-induced sediment transport and BBL hydrodynamics in an idealized estuary with a constant depth. The focus was placed on description and prediction of a nepheloid layer developed in the estuary due to the coupling effect of the seawater and resuspended sediment concentration. The basic terms used in this paper are explained in Fig. 1. As the composition of sediments in estuaries is dominantly mud, the sediment class studied here consists of the fine materials of clay with the grain size in order of several micrometers. The sediment distributions, fluxes, and estuarine BBL hydrodynamics were examined by numerical case studies that considered both neutrally stratified and stably stratified BBLs due to the resuspended sediment concentrations, with and without freshwater runoffs. Sediment-induced stratification was introduced to the water column by coupling the sediment concentration and the seawater density. This approach was adopted by previous researchers in their studies of sediment-laden BBLs of steady unidirectional flows over flat seabeds (e.g., Taylor and Dyer 1977; Smith and McLean 1977; Adams and Weatherly 1981; Anwar 1983; Soulsby and Wainwright 1987; Glenn and Grant 1987; Trowbridge and Kineke 1994). In recent studies of the hyperpcynal plumes (sediment-induced plumes) on the continental shelves and in the deep basins, the seawater density was also assumed to be influenced by sediment concentration (Chao 1998; Fohrmann et al. 1998; Kampf et al. 1999). However, these studies have not considered the reducing effect of BBL stratification on the bottom stress parameterization through the bottom drag coefficient. The novel methodology developed in this paper is as follows. 1) The study of the sediment-laden BBL was conducted in a tidal estuary of transient flow environment and 2) the slip bottom boundary condition used by the hydrodynamic model was modified in order to fully consider the effects of sediment-induced stratification on the BBL hydrodynamics.

The paper is constructed as follows. The details of the numerical model including the hydrodynamic and the sediment transport component are described in section 2. Section 3 provides a description of the experiment set up. The effects that are studied by these experiments are also introduced in this section. Section 4 presents the analysis as well as the discussions of the model results. The summary and conclusions of the study is offered in section 5.

2. Model description

a. Hydrodynamic model

The three-dimensional Princeton Ocean Model (Blumberg and Mellor 1983, 1987) was used for the numerical simulations. The numerical model solves the primitive equations for momentum, temperature, and salinity on the Arakawa C grid in the horizontal and a σ-coordinate system in the vertical. The level-2.5 turbulence closure scheme described by Mellor and Yamada (1974, 1982) was used to calculate eddy viscosity and diffusivity. The horizontal diffusivity was calculated using the Smagorinsky diffusion scheme, assuming that the horizontal diffusivity of momentum, temperature, and salinity are equal. The maximum diffusivity is estimated to be 10 m2 s−1 in the model domain. The full set of model equations is described in Blumberg and Mellor (1983, 1987). In our model, the Coriolis parameter f was set to be −0.8 × 10−4 s−1 corresponding to an estuary at a latitude of 35° in the Southern Hemisphere. The model temperature was set to a constant value of 15°C, and the model salinity was also set to a constant of 35 psu when there is no river runoff. The choice of these temperature and salinity values represents well-mixed winter estuaries during dry seasons found in southeast coast of Australia.

Density of clear seawater (without sediment contribution) is determined by the equation of state (Mellor 1998). When the contribution of the resuspended sediments was considered to study the nepheloid layer dynamics, the seawater density was calculated by a volumetric relation
i1520-0485-32-11-3113-e1
where ρw is clear seawater density, ρs is sediment density, and C is resuspended sediment concentration.

1) Model domain

Shown in Fig. 1 is the model domain. The horizontal resolution of the model is 500 m. The time steps for external and internal modes were 3 and 30 s, respectively. In the along-estuary direction, 120 grid points were taken. In the cross-estuary direction, 10 grid points were used. At the entrance to the estuary, the surface elevation was specified for the model forcing, and was not varied in the cross-estuary direction. At the head of estuary, a surface salt flux boundary condition was used if the freshwater runoff is considered by the model:
i1520-0485-32-11-3113-e2
where Kh is the vertical eddy diffusivity coefficient, S is the salinity, and R is the river flow rate set to a constant value of 800 m3 s−1.

The model used 20 sigma levels in the vertical with four logarithmically distributed layers near the surface (σ = 0.0, −0.018, −0.036, −0.071) and five logarithmically distributed layers near the bottom (σ = −0.929, −0.964, −0.982, −0.991, −1.0). The rest of the vertical sigma layers were evenly spaced with an increment of 0.071. The higher vertical resolution was necessary in the bottom boundary layer so that the dynamics of the BBL can be accurately simulated.

2) The bottom boundary conditions

At the sea surface, the fluxes of heat and momentum were assumed to vanish. At the bottom boundary, heat and salt was adiabatic, and boundary condition for the bottom velocity was
i1520-0485-32-11-3113-e3
where Km is the vertical eddy viscosity coefficient, u is the current velocity with an along-estuary component u and a cross-estuary component υ, and τb is the bottom stress and expressed as
τbρCdubub
The bottom drag coefficient Cd is specified to match the law of the wall in the bottom logarithmic layer where the water is neutrally stratified:
i1520-0485-32-11-3113-e5
Here κ is the von Kármán constant (=0.4), z0 is the bottom roughness set equal to 0.001 m for the clay bottom, and ub is the bottom (z = zb) current velocity.
In a sediment-laden bottom boundary layer, resuspended sediment stratification modifies the BBL dynamics. The velocity profile in a stratified logarithmic layer is given by
i1520-0485-32-11-3113-e6
where u∗ = (τb/ρ)1/2 is bottom friction velocity (Adams and Weatherly 1981). The effect of stratification is considered by a stability function (1 + ARf)−1, where A is an empirical constant and Rf is a flux Richardson number. Adams and Weatherly (1981) determined A = 5.5 for a sediment-laden oceanic bottom boundary layer. In a strongly stratified classic estuary where surface to bottom salinity differs by more than several practical salinity units, Anwar (1983) found that the value of A ranges from 6.8 to 14.7 and is independent of flow state and Rf. Glenn and Grant (1987) used a value of 4.7 in their study of combined wave and current flow in the suspended sediment stratified bottom boundary layer. This value was initially derived from a thermally stratified atmospheric boundary (Businger et al. 1971), but has been widely used in estuarine and coastal environment (Smith and McLean 1977; Soulsby and Wainwright 1987). We here have adopted a value of A = 5.5 for a weakly stratified estuary due to the coupling effect of the water density and the resuspended sediment concentration. A similar value (A = 5.2) was also used by Taylor and Dyer (1977).
According to Mellor and Yamada (1974), the flux Richardson number Rf can be calculated by the gradient Richardson number Ri in the level-2 closure scheme; thus
i1520-0485-32-11-3113-e7
where ∂ρ/∂z is the vertical density gradient minus the adiabatic lapse rate.
Substitute (6) into (3) and (4), the bottom drag coefficient in a sediment laden bottom boundary layer can be given by
i1520-0485-32-11-3113-e9
When the sediment contribution to the seawater density is not considered, the BBL is neutrally stratified and Rf = 0. Equation (9) reverts back to the traditional formulation of Cd described by (5). When the BBL is stratified due to the resuspended sediments (Rf > 0), the turbulence is reduced in the BBL. According to (9) the bottom drag coefficient is also reduced, leading to a “slippery” bottom boundary layer (MacCready and Rhines 1993). Finally, as Rf approaches a critical value of Rfc, the turbulence is completely suppressed by the stratification according to Mellor–Yamada Level-2 scheme. The bottom drag coefficient reaches a minimum value.

Mellor and Yamada (1974) referred to laboratory data of neutral flow in the bottom boundary layer to determine five master mixing-length-related empirical constants and found Rfc = 0.21. This value is slightly modified (Rfc = 0.19) by the same authors (Mellor and Yamada 1982) after their reworking of the data. In our study (7), (8), and (9) were used in all model experiments to estimate the bottom stress expressed by (4). A value of 0.21 was chosen for Rfc to represent a “slippery” BBL stratified by the suspended sediments. We note that Mellor–Yamada turbulent closure schemes (1974 and 1982) are derived from neutral boundary layer data, and the stratification of the boundary layers may be over estimated by these schemes according to Mellor (2001). Further discussion on the model sensitivity to the turbulence closure assumptions will follow.

b. Sediment transport model

We consider single-sized cohesive sediments of clay with a constant settling velocity ws. The three-dimensional equation describing the sediment transport in the water column is given by
i1520-0485-32-11-3113-e10
where w is the vertical water velocity. The vertical eddy diffusivity for C was set to be equal to Kh, and FC is the horizontal diffusion term parameterized according to Smagorinsky diffusion scheme. A first-order upstream scheme with iterative Smolarkiewicz antidiffusive scheme (Smolarkiewicz 1984) was used for sediment advection in (10).

Because we assumed that the resuspended sediment particle velocity only differs from the water velocity by ws in the vertical direction, the settling velocity ws is not changed in (10) after its conversion into a σ-coordinate system (Wang and Pinardi 2002, manuscript submitted to J. Geophys. Res.; Wang 2001).

The surface and lateral sediment inputs for the estuary were not considered, and the bottom boundary condition for Eq. (10) is
i1520-0485-32-11-3113-e11
where E is the net sediment flux due to deposition or resuspension.
According to Ariathurai and Krone (1976), the net sediment flux E can be formulated as follows:
i1520-0485-32-11-3113-e12
where E0 is the erosion coefficient, τc is the critical stress for resuspension and deposition, and Cb is the sediment concentration at the model bottom layer.

There is considerable uncertainty involved with the choice of E0 in (12), as it is determined by the empirical values of sediment entrainment rate and the bed load. As we are interested in qualitative description of the BBL characteristics and the sediment transport processes in an idealized tidal estuary, the exact values in sediment concentration and flux are of secondary importance. We therefore set E0 to a constant of 10−4 kg m−2 s−1. This value is similar to the one used by Clark and Elliot (1998) in their study of sediment resuspension in the Firth of Forth, Scotland. A constant E0 assumes there is an unlimited sediment bed load for resuspension.

c. Model parameters

The sediment transport model described by (10), (11), and (12) involves parameters of the settling velocity ws, and the critical stress for resuspension and deposition τc. For cohesive sediments of clay with a sediment density ρs = 1100 kg m−3 in estuaries, we have chosen a typical value of ws = −1 × 10−4 m s−1 (Trowbridge and Kineke 1994). Sensitivity test and flocculation effect on the settling velocity will also be carried out.

For a freshly deposited muddy bed, we assume τc to be 0.02 N m−2. This value is at low end of the range found in the laboratory experiments (Sheng 1984), and is equivalent to a critical friction velocity uc of 0.44 cm s−1 for resuspension and deposition. Table 1 lists the important model parameters.

3. Experimental setup

Seven numerical experiments were conducted and are listed in Table 2. Additional model runs to evaluate the sensitivity of the model to Mellor–Yamada turbulence closure assumptions, and the effect of sediment flocculation, will be discussed later. All numerical experiments were forced by the tidal elevation at the estuary entrance given by
i1520-0485-32-11-3113-e13
where TM2 and TS2 are periods for M2 and S2 tides, and aM2 and aS2 are tidal amplitudes. The numerical experiments started from rest and were run for an initial 5 days to spin up the model. After the initializing phase, the model was further integrated for another 30 days with the sediment transport submodel included. Two spring–neap tidal cycles were then covered by the model simulation period.

The first experiment was designed to compare sediment distribtuion and flux, and BBL characteristics in a neutrally stratified and a sediment-stratified estuary. Experiment 1 consists of two model runs. In the first run (expt 1a), the seawater density was not affected by the resuspended sediments. In the second run (expt 1b) the seawater density was calculated according to (1). A sediment settling velocity of ws = 1 × 10−4 m s−1 was used in this experiment, and aM2 and aS2 are equal to 0.4 and 0.1 m, respectively.

Experiment 2 examines the effect of the settling velocity on the sediment stratified BBL properties. Experiment 1b was repeated in experiments 2a and 2b with different settling velocities of ws = 5 × 10−5 m s−1 and ws = 2 × 10−4 m s−1, respectively.

Experiment 3 is similar to experiment 1 except that river runoff is added to the model forcing for both model runs. A positive buoyancy input into the model establishes haloclines that will affect the BBL properties and sediment resuspension. These effects will be studied.

Experiment 4 repeated experiment 1b using different levels of tidal forcing in order to investigate the generation and variability of cross-estuary flows of the hyperpycnal plumes. The amplitudes of spring tides were varied by choosing different aM2 values of 0.3 m in experiment 4a and 0.5 m in experiment 4b, respectively. Experiment 5 duplicated experiment 1b and experiment 4 with a reduced settling velocity ws = 5 × 10−5 m s−1.

Finally, experiments 6 and 7 were conducted to test the model sensitivity to vertical resolutions. Each experiment consisted of two model runs in which C and ρ was either decoupled or coupled. In experiment 6, twenty σ levels with linear distribution were used and the ratio of bottom layer thickness to bottom roughness length (zb + H)/z0 was equal to 1000. In experiment 7, five σ levels with linear distribution were used and the ratio of bottom layer thickness to bottom roughness length (zb + H)/z0 was increased to 4000.

Sediment distribution and flux in the estuary will be described by suspended sediment concentration C and along-estuary horizontal sediment flux Q(=uC). The description of BBL properties will be focused on the flux Richardson number Rf and friction velocity u∗. The former is given by (7) and is an approximation to the Monin–Obukhov stability parameter that quantifies stratification in the BBLs. The latter relates to the bottom shear stress and can be alternatively defined as
i1520-0485-32-11-3113-eq1
In this study this definition is expanded and u∗ is also used to describe the shear stress in the water column to indicate the level of turbulent intensity.

4. Model results

a. Effects of sediment-induced stratification on sediment distribution, flux, and BBL response

Total sediment transport load simulated by experiment 1 shows a clear spring–neap tidal cycle (Fig. 2). A phase lag of 50 h between maximum transport and the peak of the spring tides is caused by a delay in the sediment particle settling when the water density is not affected by the concentration. The sediment transport is reduced by 90% when the water column is stratified by the resuspended sediments. The tidal mean sediment transport predicted by the both model runs is negligible across the section.

When the seawater density is not affected by the sediment resuspension, sediments are resuspended to the surface. The concentration and flux are vertically homogenous and increased along the estuary toward the entrance (Fig. 3a). When the sediment contribution to the density is considered, the resuspended sediments stratify the water column. The bottom stress is reduced by the stratification. Both the sediment distribution and flux are significantly different to those from experiment 1a. The resuspended sediments are distributed near the bottom, thus the sediment flux is bottom intensified (Fig. 3b). An hyperpycnal plume is established for x > 20 km due to an along-estuary gradient in sediment concentration there.

Figure 4 shows a BBL in the lower part of estuary characterized by low Rf and high u∗ values. The depth of the BBL is on the order of several meters with an increasing thickness toward the entrance predicted by experiment 1a (Fig. 4a). In experiment 1b the depth of the BBL is reduced to less than 1 m and its thickness decreases with an increase in x due to a stronger sediment-induced stratification there (Fig. 4b). A lutocline with high Rf and low u∗ can be observed above the bottom boundary layer for x > 20 km. As the nepheloid layer beneath it increases its vertical concentration gradient towards the entrance, the depth of the lutocline decreases.

When the sediment contribution to the water density is not considered, the sediments are resuspended to the surface as previously discussed and again shown in Fig. 5a. Reoccurring high values in the near bottom sediment concentration within a semidiurnal tidal cycle is driven by the flood and ebb tides, while the semidiurnal oscillation of the concentration in the upper water column is due to the upstream advection of tides. This suggests that the sediment distribution in the BBL is dominantly affected by the vertical eddy diffusion whereas above the BBL it is primarily controlled by the horizontal advection.

When the sediment contribution to the water density is considered, the resuspended sediments are distributed only in the bottom layer with a thickness of a few meters (Fig. 5b). In addition to the tidally driven quarter-diurnal oscillation in the sediment concentration, there are some resuspension events during the spring tide that give abnormally high sediment concentration values. The frequency of these unusual resuspension events is lower than that of the tidal forcing. We refer to this phenomenon as the sediment resuspension hysteresis. The process that controls the occurrence of resuspension hysteresis in a sediment-stratified BBL needs to be further investigated.

b. Resuspension hysteresis—The nepheloid layer

In order to understand the mechanism that controls the sediment resuspension hysteresis process, Fig. 6 magnifies Fig. 5b for the period between day 22 and 26. From Fig. 6, the frequency of the hysterisis is about one day, and it occurs over one tidal cycle starting from an ebb tide. The cause of the resuspension hysteresis and the process that governs the frequency of its occurrence can be explained by Fig. 7. A resuspension event establishes a nepheloid layer, above which a lutocline is formed at a depth between 10 and 15 m with high Rf and low u∗. This lutocline descends as the nepheloid layer settles with a same rate controlled by both the sediment settling velocity and the vertical eddy diffusion. The descending rate of the lutocline is manifested by the slope of high Rf value in Fig. 7. The sediment concentration gradient of this sinking layer is modified by the tidal-induced resuspension and deposition events. Moreover, as the nepheloid layer lowers, convective mixing due to sediment-voided low density water causes a trail of low Rf and high u∗ behind.

When the lutocline reaches the near bottom depth at a stratification favorable ebb tide, the depth of the underling BBL becomes thin. This thinned BBL can be seen by a flattened near-bottom u∗ contours of reduced values in Fig. 7. The resuspension of the sediments at the ebb tide thus creates the first strong sediment concentration peak seen in the resuspension hysteresis. The voiding of the resuspended sediments due to the lowering nepheloid layer destabilizes the water column above it. The total depth of the sediment layer is then increased (Fig. 6). A second peak in the sediment concentration is followed as the BBL becomes even thinner at the following flood tide. The subsequent deposition at the high tide completely settles the nepheloid layer and sets up a condition for a less stratified and thicker BBL. A new lutocline is then established in the water column during the next resuspension event, and will eventually lead to the following resuspension hysteresis.

As we have discussed earlier, both the sediment settling velocity and the vertical eddy diffusion generated in the BBL determines the slope of Rf in Fig. 7, and consequently controls the frequency of the resuspension hysteresis. As the bottom stress is weaker at x = 25 km, there is less resuspension of the sediments that affect the water stratification. Therefore the turbulent kinetic energy is able to penetrate more deeply into the interior of the water column and reduces the sinking rate of the lutocline. This can be seen in Fig. 8a, which shows the large and elongated u∗ contours near the bottom and a gentler Rf slope than those simulated at x = 30 km. Thus the resuspension hysteresis occurs less frequently there. In contrary, a thinner BBL at x = 40 km gives a faster sinking rate of the lutocline and the resuspension hysteresis happens more frequently (Fig. 8b).

To further support our argument above, experiment 1b was repeated in experiments 2a and 2b with different settling velocity of ws = 5 × 10−5 and −2 × 10−4 m s−1, respectively. As the ws decreases (increases) the descending rate of the lutocline reduced (strengthened), characterized by the gentler (steeper) Rf and u∗ slopes (Figs. 9a,b). For completeness, Fig. 9c shows that no lutocline is developed in experiment 1a and the BBL depth is significantly larger than the model runs that consider the coupling effect.

Resuspension hysteresis occurs when the depth of the BBL is significantly reduced by the overlying lutocline as it settles. The sediment concentration in the BBL can increase abnormally during its occurrence. We can further demonstrate this process in Fig. 10. As the bottom stress or the sediment settling velocity increases (Figs. 10c,e) from those in Fig. 10b, resuspension hysteresis events occur more frequently. Thus, the distribution of the bottom values of C shown in Figs. 10c and 10e is more scattered than that shown in Fig. 10b.

As the bottom stress or the sediment settling velocity is reduced (Figs. 10a,d), resuspension hysteresis events occur less frequently. The distribution of the bottom C is less deviated from the mean value than that in Fig. 10b.

It is notable that an increase (decrease) of the sediment settling velocity decreases (increases) the minimum bottom sediment concentration (Figs. 10b,d,e). A decrease in the bottom stress also decreases the bottom sediment concentration (Figs. 10a–c).

The vertical structure of the sediment distribution indicates a thin and highly concentrated bottom layer that is overlain by a thicker layer with much smaller concentrations at times of resuspension hysteresis (Figs. 10b,c,e). This two-layer structure of sediment concentration profiles has been intermittently observed at the maximum ebb or flood tides over the continental shelf off the mouth of the Amazon River during the AMASSEDS experiment. Suspended sediment concentration profiles with the concentrations exceeding 10 g L−1 showed that there existed a thin wall layer (∼1 m) in which sediment concentration is one to two orders of magnitude larger than that in the overlying thicker layer with a depth of about 10 m (Trowbridge and Kineke 1994). In their study of the fluid muds on the Amazon shelf, Trowbridge and Kineke (1994) used a one-dimensional turbulence closure model with zero bottom sediment flux boundary condition and successfully modeled sediment profiles in the top layer. However, their study explicitly excluded the thinner highly concentrated lower layer in their model, and the sediment transport processes within this layer were not studied.

1) Sensitivity to Mellor–Yamada turbulent closure assumptions

As we noted earlier that the hypotheses and nondimensional constants of Mellor–Yamada turbulent closure schemes (1974, 1982) are all based on neutral boundary data, the extension to stratified flows is entirely a derived result. The work by Martin (1985) indeed shows that traditional Mellor–Yamada schemes overpredict turbulent dissipation so that the model produces an overly shallow, stable summertime surface layer. Dickey and Mellor (1980) used laboratory experiments and showed that the turbulence in stratified fluid decayed as in the unstratified case until a critical Richardson number GHc was reached. Guided by the laboratory data, Mellor (2001) modified Mellor–Yamada schemes by introducing a Richardson-number-dependent dissipation. Thus, the values of B1 and B2 (two of the five mixing-length-related empirical constants in the turbulent closure scheme) are corrected and become the functions of the Richardson number.

A new model run was conducted to test model sensitivity to the closure assumptions. This run is similar to experiment 1b except that corrected Mellor–Yamada turbulent scheme was used according to Mellor (2001). Here GHc was chosen to be −6, as suggested by Mellor (2001). Other values (GHc = −4, −8) are also used, however the results are not sensitive to the choice of GHc values as reported by Ezer (2000). The model-simulated sediment distribution in the water column is shown in Fig. 10f. The distribution is not significantly changed from that predicted by experiment 1b (Fig. 10b). However, because of the reduced turbulent dissipation, the increased mixing is responsible for the increased depth of the bottom layer where the resuspension hysteresis take place.

2) Effects of sediment flocculation

As shown in Fig. 10, sediment concentration in the bottom wall layer can reach as high as 1 g L−1 during the resuspension hysteresis events. Given that the estuarine clays are the primary focus of this study, the clay particles are likely to form larger grains through flocculation. As the result, the sediment settling velocity is to increase. For cohesive mud in estuaries, Mehta (1984) found that the values of settling velocity are dependent on sediment concentration, and can be described by a power law:
wsC1.3
According to (14), for values of C ∼ 1 g L−1, −ws will increase to about 10−3 m s−1.

In order to test the effects of flocculation on the model results, we replaced the constant settling velocity of ws = −10−4 m s−1 in experiment 1b with (14). The minimum settling velocity was set to be 10−5 m s−1. The model simulated sediment distribution in the water column is shown in Fig. 10g. The sediment distribution pattern for this period is a combination of those shown in Figs. 10d,e. This is easy to understand. The increased sediment settling velocity, of course, due to (14) during the resuspension events increased the frequency of resuspension hysteresis occurrence; therefore the sediment concentration values in the bottom wall layer are more scattered (similar to Fig. 10e). When the concentration is low in the water column, the settling velocity is reduced, and thus the minimum sediment concentration values near the bottom are increased (similar to Fig. 10d).

3) Effects of freshwater runoffs

In order to assess the sediment distribution and flux in the estuary under both tidal and freshwater buoyancy forcing, Experiment 1 was repeated in experiment 3 with a river flow rate of 800 m3 s−1 included in the model runs. A river-induced halocline marked by the high value of Rf is evident at the subsurface from experiment 3a (Fig. 11a). In comparison with experiment 1a, the presence of the halocline has reduced the thickness of the BBL. A higher sediment concentration is then predicted at the water depth below the halocline, as well as a higher total sediment flux across the section of x = 30 km. Because of the estuarine circulation driven by the river runoff, a spring tidal mean total sediment transport of 209 kg s−1 is predicted with an upstream direction at the cross section. This mean transport is about 10% of the maximum flux predicted at the spring tide.

When the sediment concentration and the water density is coupled, the halocline dominates the water stratification for x < 30 km (Fig. 11b). In the lower part of the estuary (x > 30 km), overturning of the surface high-salinity water advected upstream by the flood tide destabilizes the halocline and weakens the lutocline below it. Therefore the sediments are resuspended higher in the water column with respect to that predicted by experiment 1b. At x = 30 km, the halocline has eliminated the lutocline, therefore no resuspension hysteresis is occurred there (figure not shown). Furthermore, a spring tidal mean total sediment transport of 13 kg s−1 in upstream direction is predicted, which is 16% of the maximum transport at the spring tide. The instantaneous sediment flux is not significantly changed from that predicted by the experiment 1b.

c. Hyperpycnal plume

When the sediment contribution to the water density is considered, a sediment hyperpycnal plume is established for x > 20 km in the estuary where resuspension of sediments occurs. Tidal mean currents are generated by the horizontal density gradient associated with the plume. In the steady-state momentum equations that govern the mean flow in the estuary, the nonlinear terms are at least an order of the magnitude less than the other terms in the equations and can be neglected. The cross-estuary mean currents υ were obtained by solving a linearized x-direction momentum equation averaged over a tidal period
i1520-0485-32-11-3113-e15
where C and τzx are the tidal mean sediment concentration and the shear stress in x direction.

In the BBL where ∂τzx/∂z = 0 and ∂C/∂x is positive, υ is negative, indicating a cross-estuary mean current flowing to the right downstream. Its magnitude is determined by the along-estuary sediment concentration gradient. Near the surface where C ≅ 0 and thus ∂C/∂x ≅ 0, υ becomes positive due to a decreasing shear stress (∂τzx/∂z < 0) away from the bottom boundary. The vertical variability of the cross-estuary flow is demonstrated in Fig. 12. The mean flow associated with the hyperpycnal plume can be observed and has negative velocities at the bottom and positive at the surface with an order of 1 cm s−1. As the level of tidal forcing was reduced in experiment 4a (increased in expt 4b), the magnitude of the mean currents also decreased (increased) in response to a weaker (stronger) hyperpycnal plume.

Experiments 5a, 5b, and 5c repeated experiments 1b, 4a, and 4b, respectively by using a smaller settling velocity of ws = −5 × 10−5 m s−1. As the levels of the tidal forcing in experiment 5 were not changed from their corresponding runs of the previous experiments, the horizontal dimension of the plumes is not changed (Fig. 13). However, as the settling velocity of the sediments was reduced, the resuspended sediments remain in the water column longer and the concentration becomes larger. As a result, the sediment concentration gradients along the estuary are increased, and according to (15) the cross-estuary mean flows are also increased, as shown in Fig. 13.

d. Bottom drag coefficient cd

The effect of sediment stratification on the bottom drag coefficient can be observed in Fig. 14, which plots Cd versus Rf and zb according to (9). The increase of Richardson number with increasing stratification decreases bottom drag coefficient. In a strongly stratified BBL where Rf is large, Cd decreases more slowly with increasing zb, suggesting that resolution of the BBL by the model in a stratified environment becomes less critical than in a clear water case. When the water column is not stratified (Rf = 0), Cd varies from 0.01 to 0.002 for (zb + H)/z0 ranging from 60 to 5000. In experiment 1a the bottom drag coefficient remains at a near-constant value of 0.008 (Fig. 15). In contrast, the bottom drag coefficient varies significantly with time in experiment 1b. It reaches a minimum value of about 0.003 during the spring tides when the sediment-induced stratification is strong. During the neap tides when no sediments are resuspended and the water column is neutrally stratified, the bottom drag coefficient reaches a maximum of 0.008.

The variability in the bottom drag coefficient has been observed in a tidal estuary of south San Francisco Bay by Cheng et al. (1999). Detailed measurements of current profiles within 1.5 m above the seabed suggested a drag coefficient variation from 0.002 during the spring tide to 0.0065 during a neap tide. The measured tidal elevation difference between the spring and the neap tides is about 0.25 m. The authors postulated that this Cd variability was caused by the change in the bottom roughness length z0 due to sediment erosion and deposition. However, no sediment and bed form data were available to support their hypothesis, and the effect of sediment-induced stratification on hydrodynamic properties in the BBL including Cd was not included in their analysis.

As we have shown in Fig. 15, the variability of Cd in this study is caused by a change in the sediment-induced stratification from the spring to neap tides. The numerical experiment predicted a range of 0.005 in Cd variability for a spring–neap tidal cycle with Δζ equal to 0.2 m (Δζ = ζspringζneap). This result agrees with the observed Cd range of 0.0045 in south San Francisco Bay with a similar Δζ value. We note that the model-predicted Cd range could be varied with the choice of A in (9) and with the model vertical resolution. We have already shown that the model vertical resolution is insensitive to the minimum Cd values in the stratified BBL (Fig. 14). Furthermore, if a maximum observed value of A = 15 for the estuaries (Anwar 1983) was used, the model-predicted Cd range was increased to 0.007, which is still the same order of magnitude value as the one observed by Cheng et al. (1999). Given the general agreement between the model results and the observation, one speculates that it may be the sediment-induced stratification that has caused the variability in the drag coefficient in south San Francisco Bay.

A related BBL property to the drag coefficient discussed above is the bottom friction velocity u∗. In the sediment-laden BBL, u∗ will always be over estimated by fitting the measured velocity profile to a neutral logarithmic distribution. This can be demonstrated in Table 3. It is clear that u∗ can be reduced by 29% if the effect of sediment-induced stratification is considered in the model. Furthermore, as the settling velocity increases or the sediment grain size increases, the bottom friction velocity decreases. This agrees with Soulsby and Wainwright (1987) who found a similar relationship between u∗ and grain size for clay and silt at a sediment-laden bottom, as described in Fig. 1b of their paper.

Table 3 also shows the sensitivity of the model results to the corrected Mellor–Yamada (M–Y) turbulent closure scheme and to the effect of clay flocculation. The model predicted u∗ increases slightly due to an increased turbulence when it is compared with the uncorrected Mellor-Yamada turbulence scheme. When the effect of flocculation is considered, the settling velocity is increased at the spring flood tide, thus the value of u∗ is decreased as shown in experiment 2b.

e. Model sensitivity to vertical resolution

In order to test the model sensitivity to vertical resolutions, experiments 6 and 7 were carried out with zb + H = 0.5 m (expt 6) and zb + H = 2.5 m (expt 7), respectively. These experiments showed that the current velocities are less sensitive to the decreasing model resolutions than the suspended sediment concentration. When the model vertical resolution was reduced, higher eddy diffusivity was predicted in the BBL. As a result, the vertical sediment decay rates are reduced in comparison with those predicted by experiment 1. The maximum resuspended sediment concentration at a spring tide was overpredicted by as much as 15% in the water column by both experiments (figure not shown) in comparison with that predicted by experiment 1.

5. Summary and conclusions

The Princeton Ocean Model was coupled with a sediment transport model to study sediment resuspension and the BBL hydrodynamics in an idealized tidal estuary that has a constant water depth and a muddy bed. A semidiurnal tide with a spring–neap cycle was used to force the model at the estuary entrance. A stability function is introduced to the bottom drag coefficient Cd for a slip bottom boundary condition in order to consider the effects of sediment-induced stratification in the BBL.

When the resuspended sediments do not affect the seawater density, spring tides resuspend sediments to the surface near the estuarine entrance where the bottom stress is larger than the critical stress value. At a given location near the entrance, the reoccurring high sediment concentration values near the bottom within a semidiurnal period are due to the resuspension of sediments by the flood and ebb tides, while a semidiurnal oscillation in C is simulated in the water column. This suggests that the sediment distribution in the BBL is dominantly affected by the vertical eddy diffusion whereas above the BBL it is primarily controlled by the horizontal advection. The freshwater runoff produces a halocline that reduces the thickness of the BBL in the estuary. The sediment concentration and horizontal flux in the water column are increased as a result. A significant upstream tidal mean sediment transport is also predicted due to the river-induced estuarine circulation.

When the seawater density and the sediment concentration is coupled, the sediment-induced stratification reduces the bottom stress and the thickness of the BBL. The sediments resuspended by the spring tides are only distributed in the bottom layer with a thickness of a few meters. Thus a significantly smaller horizontal sediment transport is predicted in comparison with the decoupled model run. A lutocline, characterized by high value in Rf and low value in u∗, is established above the BBL due to a maximum vertical sediment concentration gradient there. As the nepheloid layer beneath it settles to the bottom at a rate controlled by the sediment settling velocity and the vertical eddy diffusivity, the depth of the BBL is reduced by the sinking lutocline and the sediment concentration is abnormally increased during a resuspension event. The frequency of this unusual resuspension event is commanded by the nepheloid layer settling rate and is lower than that of the tidal forcing. We refer to this phenomenon as the sediment resuspension hysteresis. The freshwater-induced halocline may dominate the water stratification and therefore eliminate the lutocline. Under this condition no sediment resuspension hysteresis will occur, and an upstream tidal mean sediment transport may take place due to the estuarine circulation. The coupling effect of the sediment concentration and the water density may also establish an hyperpycnal plume near the estuarine entrance and generates a cross-estuary tidal mean flow in order of 1 cm s−1.

The novelty in the model development of this study is the modification of the slip bottom boundary condition by introducing a stability function to the bottom drag coefficient Cd for the numerical experiments; thus the sediment contribution to the seawater density can be considered. We showed that the sediment-induced stratification reduces the bottom drag coefficient through the stability function. As the stratification varies from spring to neap tides, the bottom drag coefficient variability is also predicted. This variability in Cd has been observed by Cheng et al. (1999) in south San Francisco Bay.

This paper describes exploratory modeling results of sediment processes in both a neutrally and sediment-induced stratified tidal estuary. The study reveals intriguing BBL processes in the nepheloid layer, such as sediment resuspension hysteresis that causes a highly concentrated fluid-mud bottom wall layer and the variability of the bottom drag coefficient. These model predicted nepheloid layer characteristics and their variability have been observed in the turbid estuarine environment; however, the processes that control them have not been understood (e.g., Trowbridge and Kineke 1994; Cheng et al. 1999). Therefore, this modeling study represents a preliminary but significant step in the direction of fully describing and predicting the complex rheology of nepheloid layers. Moreover, the development of nepheloid layers in estuaries and coastal seas can clearly inhibit the upward vertical transport of nutrients as well as pollutants trapped beneath them, and thus modify sediment transport and strata formation. If biogeochemical flux and sediment transport models could be coupled with our prediction of nepheloid layer dynamics, a more accurate representation of the primary production and the bed formation may result.

It should be finally stressed that the model prediction of sediment distribution, flux and the BBL properties in this study is tentative without direct data–model comparison. Field measurement programs of turbid bottom boundary layers are desirable in future to conduct further study on nepheloid layer dynamics.

Acknowledgments

This work is in its final form during the author's visit to the CNR–IGM/The University of Bologna supported by 2001 UNSW Special Study Program and the “Progetto Ambiente Mediteraneo” funded by an ENEA-MURST Program Agreement. Special thanks goes to Professor Nadia Pinardi, who hosted this very pleasant and productive visit, and to Mr. Marcello Vicci for his enthusiastic and constructive discussion on various research topics, including this one. Comments from Dr. Rich Signell and two anonymous referees improved the manuscript. This work was supported by a grant from the Australian Partnership for Advanced Computing (APAC) National Facility.

REFERENCES

  • Adams Jr.,, C. E., and G. L. Weatherly, 1981: Some effects of suspended sediment stratification on an oceanic bottom boundary layer. J. Geophys. Res., 86 , 41614172.

    • Search Google Scholar
    • Export Citation
  • Anwar, H. O., 1983: Turbulence measurements in stratified and well-mixed estuarine flows. Estuarine Coastal Shelf Sci., 17 , 243260.

  • Ariathurai, R., and R. B. Krone, 1976: Mathematical modelling of sediment transport in estuaries. Circulation, Sediments, and Transfer of Material in the Estuary, M. Wiley, Ed., Estuarine Processes, Vol. II, Academic Press, 98–106.

    • Search Google Scholar
    • Export Citation
  • Armi, L., and E. D'Asaro, 1980: Flow structures of the benthic ocean. J. Geophys. Res., 85 , 469484.

  • Blumberg, A. F., and G. L. Mellor, 1983: Diagnostic and prognostic numerical circulation studies of the South Atlantic Bight. J. Geophys. Res., 88 , 45794592.

    • Search Google Scholar
    • Export Citation
  • Blumberg, A. F., and G. L. Mellor, 1987: A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Models of Marine and Estuarine Dynamics, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier Oceanography Series, Vol. 45, Elsevier, 55–88.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28 , 181189.

    • Search Google Scholar
    • Export Citation
  • Chao, S-Y., 1998: Hyperpycnal and buoyant plumes from a sediment-laden river. J. Geophys. Res., 103 , 30673082.

  • Cheng, R., C-H. Ling, J. W. Gartner, and P. F. Wang, 1999: Estimates of bottom roughness length and bottom shear stress in south San Francisco Bay, California. J. Geophys. Res., 104 , 77157728.

    • Search Google Scholar
    • Export Citation
  • Clark, S., and A. J. Elliot, 1998: Modelling suspended sediment concentration in the Firth of Forth. Estuarine Coastal Shelf Sci., 47 , 235250.

    • Search Google Scholar
    • Export Citation
  • Dickey, T. D., and M. L. Mellor, 1980: Decaying turbulence in neutral and stratified fluids. J. Fluid Mech., 99 , 1331.

  • Ezer, T., 2000: On the seasonal mixed layer simulated by a basin-scale ocean model and the Mellor–Yamada turbulence scheme. J. Geophys. Res., 105 , 1684316855.

    • Search Google Scholar
    • Export Citation
  • Fohrmann, H., J. O. Backhaus, F. Laume, and J. Rumohr, 1998: Sediments in bottom-arrested gravity plumes: Numerical case studies. J. Phys. Oceanogr., 28 , 22502274.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., 1993: The importance of suppression of turbulence by stratification on the estuarine turbidity maximum. Estuaries, 16 , 113125.

    • Search Google Scholar
    • Export Citation
  • Gibbs, R. J., and L. Konwar, 1986: Congulation and settling of Amazon River suspended sediment. Cont. Shelf Res., 6 , 127149.

  • Glenn, S. M., and W. D. Grant, 1987: A suspended sediment stratification correction for combined wave and current flows. J. Geophys. Res., 92 , 82448264.

    • Search Google Scholar
    • Export Citation
  • Kampf, J., J. O. Backhaus, and H. Fohrmann, 1999: Sediment-induced slope convection: Two-dimensional numerical case studies. J. Geophys. Res., 104 , 2050920522.

    • Search Google Scholar
    • Export Citation
  • King, B., and E. Wolanski, 1996: Bottom friction reduction in turbid estuaries. Mixing in Estuaries and Coastal Studies, C. Pattiaratchi, Ed., Amer. Geophys. Union, 325–337.

    • Search Google Scholar
    • Export Citation
  • Lyne, V. D., B. Butman, and W. D. Grant, 1990a: Sediment movement along the U.S. East Coast continental shelf—I. Estimates of bottom stress using the Grant–Madsen model and near bottom wave and currents measurements. Cont. Shelf Res., 10 , 397428.

    • Search Google Scholar
    • Export Citation
  • Lyne, V. D., B. Butman, and W. D. Grant, 1990b: Sediment movement along the U.S. East Coast continental shelf—II. Modelling suspended sediment concentration and transport rate during storms. Cont. Shelf Res., 10 , 429460.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., and P. B. Rhines, 1993: Slippery bottom boundary layers on a slope. J. Phys. Oceanogr., 23 , 522.

  • Martin, P. J., 1985: Simulation of the mixed layer at OWS November and Papa with several models. J. Geophys. Res., 90 , 903916.

  • Mehta, A. J., 1984: Characterization of cohesive sediment properties and transport progresses in estuaries. Estuarine Cohesive Sediment Dynamics, A. J. Mehta, Ed., Springer-Verlag, 468 pp.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 1998: User's guide for a three-dimensional, primitive equation numerical ocean model. Princeton University Rep., 41 pp. [Available from Program in Atmospheric and Oceanic Science, Princeton University, Princeton, NJ 08544.].

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2001: One-dimensional, ocean surface layer modeling: A problem and a solution. J. Phys. Oceanogr., 31 , 790809.

  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31 , 17911806.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20 , 851875.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and X. H. Wang, 1996: Pressure compensation and the bottom boundary layer. J. Phys. Oceanogr., 26 , 22142222.

  • Oey, L-Y., G. L. Mellor, and R. I. Hires, 1985a: A three-dimensional simulation of the Hudson–Raritan estuary. Part I: Description of the model and model simulations. J. Phys. Oceanogr., 15 , 16761692.

    • Search Google Scholar
    • Export Citation
  • Oey, L-Y., G. L. Mellor, and R. I. Hires, 1985b: A three-dimensional simulation of the Hudson–Raritan estuary. Part II: Comparison with observation. J. Phys. Oceanogr., 15 , 16931709.

    • Search Google Scholar
    • Export Citation
  • Sangiorgi, F., R. Setti, G. Gabbianelli, and C. Trombini, 1998: Geochemical characterisation of Hg-contaminated sediments of the “Pialassa Baiona” (Ravenna Lagoon, Italy). Rapp. Comm. Int. Explor. Sci. Mer Mediterr., 35 , 9697.

    • Search Google Scholar
    • Export Citation
  • Sheng, Y. P., 1984: Modelling bottom boundary layer and cohesive sediment dynamics in estuarine and coastal waters. Estuarine Cohesive Sediment Dynamics, A. J. Mehta, Ed., Springer-Verlag, 360–400.

    • Search Google Scholar
    • Export Citation
  • Smith, J. D., and S. R. McLean, 1977: Spatially averaged flow over a wavy surface. J. Geophys. Res., 82 , 17351746.

  • Smolarkiewicz, P. K., 1984: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comput. Phys., 54 , 325362.

    • Search Google Scholar
    • Export Citation
  • Soulsby, R. L., and B. L. S. A. Wainwright, 1987: A criterion for the effect of suspended sediment on near-bottom velocity profiles. J. Hydraul. Res., 25 , 341356.

    • Search Google Scholar
    • Export Citation
  • Taylor, P. A., and K. R. Dyer, 1977: Theoretical models of flow near the bed and their implications for sediment transport. The Sea, E. D. Goldberg, Ed., Vol. 6, Marine Modeling, Wiley and Sons, 579–601.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., and S. J. Lentz, 1991: Asymmetric behavior of the oceanic boundary layer above a sloping bottom. J. Phys. Oceanogr., 21 , 11711185.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., and G. C. Kineke, 1994: Structure and dynamics of fluid muds over the Amazon continental shelf. J. Geophys. Res., 99 , 865874.

    • Search Google Scholar
    • Export Citation
  • van Rijn, L. C., 1984: Sediment transport. Part II: Suspended load transport. J. Hydraul. Eng., ASCE, 110 , 16131641.

  • Wang, X. H., 2001: A numerical study of sediment transport in a coastal embayment during winter storms. J. Coastal Res., 34 (Special Issue) 414427.

    • Search Google Scholar
    • Export Citation
  • Wang, X. H., and P. D. Craig, 1993: An analytic model of tidal circulation in a narrow estuary. J. Mar. Res., 51 , 447465.

  • Weatherly, G. L., and P. J. Martin, 1978: On the structure and dynamics of the oceanic bottom boundary layer. J. Phys. Oceanogr., 8 , 557570.

    • Search Google Scholar
    • Export Citation
  • Wright, L. D., W. J. Wiseman Jr.,, Z-S. Yang, B. D. Bornhold, G. H. Keller, D. B. Prior, and J. N. Suhayda, 1990: Processes of marine dispersal and deposition of suspended silts off the modern mouth of the Huanghe (Yellow River). Cont. Shelf Res., 10 , 140.

    • Search Google Scholar
    • Export Citation
  • Zavatarelli, M., and G. L. Mellor, 1995: A numerical study of the Mediterranean Sea circulation. J. Phys. Oceanogr., 25 , 13841414.

Fig. 1.
Fig. 1.

Schematic explanation of basic terms and the model domain of an idealized estuary

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 2.
Fig. 2.

Time series of the tidal elevation and the total sediment transport across the section at x = 30 km, predicted by expt 1a (thin line) and expt 1b (thick line)

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 3.
Fig. 3.

Sediment concentration C and horizontal flux Q for spring flood tide (t = 25 days) along an axial cross section in the estuary. The actual model domain extends 10 km farther downstream. The cross-estuary variations in C and Q predicted by the model are negligible. (a) Model prediction from expt 1a and (b) model prediction from expt 1b. The negative flux indicates an upstream sediment transport by the flood tide

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 2 but for the flux Richardson number Rf and friction velocity u∗. A five-point Laplacian spatial filter is applied to both Rf and u∗ in order to remove smaller-scale noise

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 5.
Fig. 5.

Vertical and temporal variation of sediment concentration C and the horizontal flux Q at x = 30 km, predicted by (a) expt 1a and (b) expt 1b for the second spring–neap tidal cycle. Positive Q indicates sediment transport downstream and is denoted by the solid lines

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 6.
Fig. 6.

Vertical and temporal variation of sediment concentration C and the horizontal flux Q at x = 30 km from day 22 to 26, predicted by expt 1b. Positive Q indicates sediment transport downstream and is denoted by the solid lines

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 7.
Fig. 7.

Vertical and temporal variation of the flux Richardson number Rf and friction velocity u∗ at x = 30 km from day 22 to 26, predicted by expt 1b

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 8.
Fig. 8.

As in Fig. 7 but for (a) x = 25 km and (b) x = 40 km.

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 7 but predicted by (a) expt 2a, (b) expt 2b, and (c) expt 1a.

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 9.
Fig. 9.

(Continued)

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 10.
Fig. 10.

Sediment distribution in the water column for the period from day 22 to 26. The sediment concentration was predicted by expt 1b at (a) x = 25 km, (b) x = 30 km, (c) x = 40 km; (d) expt 2a at x = 30 km; (e) expt 2b at x = 30 km; (f) expt 1b with corrected M–Y turbulence scheme at x = 30 km; and (g) expt 1b with the effect of sediment particle flocculation at x = 30 km

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 11.
Fig. 11.

The flux Richardson number Rf for spring flood tide (t = 25 days) along an axial cross section in the estuary predicted by (a) expt 3a and (b) expt 3b. A five-point Laplacian spatial filter is applied to both Rf and u

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 12.
Fig. 12.

Spring–tidal mean sediment concentration C and cross-estuary velocity υ along an axial cross-section in the estuary; C and υ are averaged over 10 days (5 days before and after the spring tide). (a) Model prediction from expt 1b, (b) model prediction from expt 4a, and (c) model prediction from expt 4b. Negative velocity indicates a current flowing out of the page.

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 13.
Fig. 13.

As in Fig. 12 but for expt 5. (a) Model prediction from expt 5a, (b) model prediction from expt 5b, and (c) model prediction from expt 5c.

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 14.
Fig. 14.

The effect of sediment stratification and the model vertical resolution on the bottom drag coefficient Cd

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Fig. 15.
Fig. 15.

Time series of the tidal mean bottom drag coefficient at x = 30 km, predicted by expt 1a (thin line) and expt 1b (thick line)

Citation: Journal of Physical Oceanography 32, 11; 10.1175/1520-0485(2002)032<3113:TISRAT>2.0.CO;2

Table 1. 

Parameters for sediment transport model

Table 1. 
Table 2. 

Setup of numerical experiments

Table 2. 
Table 3. 

Model-predicted bottom friction velocity u* at spring flood tide (t = 25 days) at x = 30 km

Table 3. 
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