Influence of asymmetric tidal mixing on sediment dynamics in a partially mixed estuary

Zhongyong Yang Zhiming Liang Yufeng Ren Daobin Ji Hualong Luan Changwen Li Yujie Cui Andreas Lorke

Zhongyong Yang, Zhiming Liang, Yufeng Ren, Daobin Ji, Hualong Luan, Changwen Li, Yujie Cui, Andreas Lorke. Influence of asymmetric tidal mixing on sediment dynamics in a partially mixed estuary[J]. Acta Oceanologica Sinica, 2023, 42(9): 1-15. doi: 10.1007/s13131-023-2159-9
Citation: Zhongyong Yang, Zhiming Liang, Yufeng Ren, Daobin Ji, Hualong Luan, Changwen Li, Yujie Cui, Andreas Lorke. Influence of asymmetric tidal mixing on sediment dynamics in a partially mixed estuary[J]. Acta Oceanologica Sinica, 2023, 42(9): 1-15. doi: 10.1007/s13131-023-2159-9

doi: 10.1007/s13131-023-2159-9

Influence of asymmetric tidal mixing on sediment dynamics in a partially mixed estuary

Funds: The National Natural Science Foundation of China under contract Nos U2040220, 52079069, 52009066, 52379069, 52009079, 42006156 and U2240220; the CRSRI Open Research Program under contract No. CKWV20221003/KY; the Open Research Program of Hubei Key Laboratory of Intelligent Yangtze and Hydroelectric Science under contract No. ZH2102000109; the Outstanding Young and Middle-aged Scientific and Technological Innovation Team in Universities of Hubei Province under contract No. T2021003; the Hubei Province Chutian Scholar Program (granted to Andreas Lorke).
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  • Figure  1.  Site map of the York River Estuary showing the location of field observations. A sketch map of the model geometry attached in the top-right corner, where $ z=\eta $ is the elevation of the water surface and $ z=-H $ is the bed. The horizontal dashed line indicates the average sea level (z = 0), while the solid line shows surface elevation during a tidal period of length P.

    Figure  2.  Model results of the vertical-temporal structure of total flow velocity (u = u0+u2) (a) and of the vertical structure of the residual components (b) based on the parameters of an observation point in the York River Estuary (Table 1). The blue line shows the flow component driven by the longitudinal density gradient ($ {u}_{0\rho } $), the green line is contribution of asymmetric tidal mixing ($ {u}_{0a} $), and the red line is the contribution from fresh water discharge ($ {u}_{0q} $). The solid black line shows the corresponding modeled mean velocity and the dashed line shows the observed mean velocity from Scully and Friedrichs (2003).

    Figure  3.  Model results (a) and observations (b, taken from Scully and Friedrichs (2003)) for the vertical-temporal structure of suspended sediment concentration (SSC) over two M2 tidal periods (~ 25 h). The line plots in panel b compares temporal variation of near bottom SSC (z = 7 m) from observations and model results. The dashed horizontal lines in panel a mark the depth range with observational data shown in panel b. The labels “F” and “E” in panel a and b denote “flood” and “ebb”, respectively. Panels c, d and e show individual components of M2 component SSC induced by bottom shear stress (c2t), M2 component SSC induced by asymmetry of diffusivity (c2a), and M4 component SSC induced by bottom shear stress (c4t), respectively. Panel f shows the vertical distribution of SSC amplitude of each component.

    Figure  4.  Vertical structure of sediment flux and its components based on the parameters for a point in the York River Estuary. $ {F}_{0a} $, $ {F}_{0\rho } $ and $ {F}_{0q} $ represent residual sediment flux related to asymmetry tidal eddy viscosity, horizontal density gradient, and river discharge. $ {F}_{2t} $ and $ {F}_{2a} $ represent tidal sediment flux related to bottom shear stress varying in M2 frequency and asymmetry tidal diffusivity. The dashed black line (YR99) shows the observed sediment flux cited from Scully and Friedrichs (2003).

    Figure  5.  Vertical-temporal structure of the asymmetric tidal mixing (ATM)-induced SSC (c2a) during a single M2 tidal period for different phase angles between tidal flow and sediment diffusivity ($ \theta $). Panels a, b, c and d represent $\theta =0,\theta =0.5\pi , $$ \theta =\pi \;\mathrm{a}\mathrm{n}\mathrm{d}\;\theta =1.5\pi$, respectively. The remaining parameters are shown in Table 1.

    Figure  6.  Vertical structure of phase lag of suspended sediment concentration in response to diffusivity phase $ \theta $ in case of: $\partial \rho /\partial x=0,{U}_{0}=0.15\;\mathrm{m}/{\mathrm{s}}$ (scenario z (i)) (a) and $\partial \rho /\partial x=1\times {10}^{-3}\;\mathrm{k}\mathrm{g}/{\mathrm{m}}^{4},{U}_{0}=0$ (scenario (ii)) (b). The black line represents the analytical result of Yu et al. (2011). The gray line shows the model results of c2t, i.e., without consideration of asymmetric tidal mixing. The remaining 4 colored lines represent the result of $ \phi \left(z\right) $ with consideration of c2a for four $ \theta $ values ($ 0, 0.5\pi ,\pi , 1.5\pi $).

    Figure  7.  Vertical structure of M2 suspended sediment concentration (SSC) component (c2) over a tidal period under four different values of phase angle of tidally varying sediment diffusivity ($ \theta $) in case of scenario (i), $\partial \rho /\partial x=0,{U}_{0}=0.15\;{\rm{m}}/{\rm{s }}$. Panels a, b, c and d show results for $\theta =0,\;\theta =0.5\pi ,\; \theta =\pi \;\mathrm{a}\mathrm{n}\mathrm{d}\;\theta =1.5\pi$, respectively.

    Figure  8.  Vertical structure of M2 suspended sediment concentration (SSC) component (c2) over a tidal period under four different values of phase angle of tidally varying sediment diffusivity ($ \theta $) in case of scenario (ii), $ \partial \rho /\partial x=1\times {10}^{-3}\; {\rm{kg}}/{{\rm{m}}}^{4},\;{U}_{0}=0 $. Panels a, b, c and d show results for $ \theta =0, \; \theta =0.5\pi ,\;\theta =\pi \;\mathrm{and}\;\theta =1.5\pi $, respectively.

    Figure  9.  Tidally mean near bottom shear stress $ \left\langle{{\tau }_{b}}\right\rangle $ (a) and sediment flux (b–i) as a function of $ \theta $ and $ \gamma =\left[{u}_{0\rho }\right]/\left[{u}_{0q}\right] $. The dashed white line indicates a ratio $ \gamma =1 $. The solid white line indicates the value $ \gamma $ for which the average shear stress $ \left\langle{{\tau }_{b}}\right\rangle=0 $. The solid red line in panel b–i indicates values of $ \gamma $ for which the sediment flux is zero. The remaining boundary conditions can be found in Table 1.

    Table  1.   Assumptions of the one-dimensional analytical model

    AssumptionExplanation
    $ \dfrac{\eta }{H}=O\left(\varepsilon\right) $water level fluctuation is an order of magnitude smaller than water depth
    $ \left(\dfrac{U_0}{U_2},\dfrac{U_d}{U_2},\dfrac{U_q}{U_2}\right)=O\left(\varepsilon\right) $residual currents are an order of magnitude smaller than tidal currents
    $ \left(\dfrac{A}{\omega H^2},\dfrac{K}{\omega H^2}\right)=O\left(1\right) $frictional force can affect the whole water column
    $ \left(\dfrac{A_2}{A_0},\dfrac{K_2}{K_0}\right)=O\left(\varepsilon\right) $the fluctuating component of eddy viscosity (diffusivity) is an order of magnitude smaller than the mean component
    $ \dfrac{w_s}{\omega H}=O\left(1\right) $length scale of sediment settling during a tidal cycle is comparable to water depth
    Note: Here, $ \left({U}_{0},{U}_{2}\right) $ represent typical values of the mean velocity and M2 tidal velocity, respectively. The parameters ${U}_{d}=g{H}^{3} \Big(\dfrac{\partial \rho }{\partial x}\Big)/ \left(48\rho A\right)$ and $ {U}_{q}=2q/\left(3H\right) $ are the typical velocity scales for residual currents driven by an along-estuary density gradient and fresh water discharge. The parameter $ \varepsilon \ll 1 $ indicates the magnitude of the difference to higher-order physical components.
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    Table  2.   Definition of symbols used in the model description

    SymbolDefinitionSymbolDefinition
    $ \omega $M2 tidal frequency$ {w}_{s} $settling velocity
    $ P $M2 tidal period$ c $SSC
    $ Ri $Richardson number$ {c}_{0} $tidally mean SSC (dominant order)
    $ s $partially slip parameter$ {c}_{4} $M4 component SSC (dominant order)
    $ \partial {\rho }/\partial {x} $along-estuary density gradient$ {c}_{2} $M2 component SSC (first order)
    $ {{q}}_{0} $fresh water discharge$ {c}_{2t} $bottom shear stress induced $ {c}_{2} $
    $ {{q}}_{2} $M2 tidal discharge$ {c}_{2a} $ATM induced $ {c}_{2} $
    $ {u} $along-estuary velocity$ {c}_{a} $reference concentration
    $ {{u}}_{2} $M2 tidal velocity (dominant order)($ A $, $ K $)eddy viscosity and eddy diffusivity
    $ {{u}}_{0} $tidally mean velocity (first order)($ {A}_{0} $, $ {K}_{0} $)tidally mean component of A and K
    $ {{u}}_{0{a}} $ATM induced u0($ {A}_{2} $, $ {K}_{2} $)M2 component of A and K
    $ {{u}}_{0{\rho }} $$ \partial \rho /\partial x $ induced $ {u}_{0} $($ \left|{A}_{2}\right| $, $ \left|{K}_{2}\right| $)amplitude of A2 and K2
    $ {{u}}_{0{q}} $fresh water discharge induced u0$ \theta $phase of A2 or K2
    Note: ATM: asymmetric tidal mixing; SSC: suspended sediment concentration.
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    Table  3.   Model input parameter values representative for a point in the York River Estuary, USA during April 1999 (referenced from Scully and Friedrichs (2003, 2007))

    QuantitySymbolValue
    Water depthH7.0 m
    Amplitude of tidal velocityU20.6 m/s
    Depth mean velocityU00.045 m/s
    Angular M2 tidal frequency$ \omega $1.4 × 10−4 s−1
    Gravitational accelerationg9.81 m/s2
    Reference density$ {\rho }_{0} $1 020 kg/m3
    *Bed to surface density difference$ \Delta \rho $2.0 kg/m3
    *Along-channel density gradient$ \partial \rho /\partial x $8.6 × 10−4 kg/m4
    *Threshold bed shear stress$ {\tau }_{c} $0.002 kg/(m·s2)
    *Settling velocityws0.6 mm/s
    *Ratio of $ \left|{K}_{2}\right|/{K}_{0} $ or $ \left|{A}_{2}\right|/{A}_{0} $$ \alpha $0.3
    *Phase lag of $ {K}_{2} $ or $ {A}_{2} $$ \theta $$ 1.4\pi $
    Note: The stars mark the parameters deduced from the above references and were modified during model validation.
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出版历程
  • 收稿日期:  2022-08-27
  • 录用日期:  2022-11-04
  • 网络出版日期:  2023-10-18
  • 刊出日期:  2023-09-01

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