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Potential morphological responses of an artificial beach to a flood in extreme events: field observation and numerical modelling
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Jiadong Fan1, Cuiping Kuang1, *, Xuejian Han1, Lixin Gong2, 3, *, Huixin Liu2, 3, Jiabo Zhang2, 3
Acta Oceanologica Sinica | 2024, 43(7) : 78 - 92
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Acta Oceanologica Sinica | 2024, 43(7): 78-92
• Ocean Engineering •
Potential morphological responses of an artificial beach to a flood in extreme events: field observation and numerical modelling
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Jiadong Fan1, Cuiping Kuang1, *, Xuejian Han1, Lixin Gong2, 3, *, Huixin Liu2, 3, Jiabo Zhang2, 3
Affiliations
  • 1 College of Civil Engineering, Tongji University, Shanghai 200082, China
  • 2 The Eighth Geological Brigade, Hebei Geological and Mineral Exploration Development Bureau, Qinhuangdao 066001, China
  • 3 Marine Ecological Restoration and Smart Ocean Engineering Research Center of Hebei Province, Qinhuangdao 066001, China
Published: 2024-07-25 doi: 10.1007/s13131-023-2184-8
Outline
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Conch Island is a typical artificial island at the Tanghe Estuary in Bohai Sea, China. To improve natural environment and boost local tourism, beach nourishment will be applied to its north-western shore. The projected beach is landward and opposite to the Jinmeng Bay Beach. Nowadays, with climate changes, frequent heavy rainfalls in Hebei Province rise flood hazards at the Tanghe Estuary. Under this circumstance, potential influences on the projected beach of a flood are investigated for sustainable managements. A multi-coupled model is established and based on the data from field observations, where wave model, flow model and multi-fraction sediment transport model are included. In addition, the impacts on the projected beach of different components in extreme events are discussed, including the spring tides, storm winds, storm waves, and sediment inputs. The numerical results indicate the following result. (1) Artificial islands protect the coasts from erosion by obstructing landward waves, but rise the deposition risks along the target shore. (2) Flood brings massive sediment inputs and leads to scours at the estuary, but the currents with high sediment concentration contribute to the accretions along the target shore. (3) The projected beach mitigates flood actions and reduces the maximum mean sediment concentration along the target shore by 20%. (4) The storm winds restrict the flood and decrease the maximum mean sediment concentration by 21%. With the combined actions of storm winds and waves, the maximum value further declines by 38%. (5) A quadratic polynomial relationship between the deposition depths and the maximum sediment inputs with flood is established for estimations on the potential morphological changes after the flood process in extreme events. For the uncertainty of estuarine floods, continuous monitoring on local hydrodynamic variations and sediment characteristics at Tanghe Estuary is necessary.

beach nourishment  /  flood  /  artificial island  /  sediment transport  /  extreme events  /  storm
Jiadong Fan, Cuiping Kuang, Xuejian Han, Lixin Gong, Huixin Liu, Jiabo Zhang. Potential morphological responses of an artificial beach to a flood in extreme events: field observation and numerical modelling[J]. Acta Oceanologica Sinica, 2024 , 43 (7) : 78 -92 . DOI: 10.1007/s13131-023-2184-8
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1 Introduction
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Nowadays, non-structural measures have been widely applied to coastal restorations (Zhong et al., 2021). In particular, beach nourishment has been proved to be an effective approach to mitigate excessive erosions and recessions along coasts of the Bohai Sea, involving Tiger-Rock Beach (Kuang et al., 2019), Jinmeng Bay Beach (Xie et al., 2013) and Beidaihe Beach (Zhang et al., 2012; Kuang et al., 2011). Moreover, nourished beaches can provide public leisure spaces to stimulate the development of coastal tourism. To attract tourists and achieve economic benefits further, artificial islands projects are popular in recent decades. However, continuous development activities not only affect functions of soft structures, but also alter local hydrodynamic conditions considerably. Researches on Chinese coasts provide massive experiences for construction and management issues of artificial islands. For instance, with the construction of Nanhaimingzhu artificial island, local dynamic conditions changes in the Haikou Bay. In details, it is found that the artificial island hinders currents and waves, and results in massive depositions in its cover areas (Xiao, 2021; Xiao et al., 2022). Meanwhile, the currents are intensified on both sides of the artificial island, which causes great erosions on the coast, so He et al. (2021) and Li (2018) suggested that beach nourishment should be utilized for essential protections, and such approach is also applicable to the Hongtang Bay in Sanya, Hainan (Li, 2021) and the Riyue Bay in Wanning, Hainan (Shi et al., 2015). According to field observations (Zhang et al., 2022; Li et al., 2019), the interactions between two artificial islands bring about much more erosions on the coast for intensive diffraction in the Riyue Bay. Apart from coasts, shores of artificial islands are also faced with the risks of erosions. For example, the flow velocities along Ruyi Island in Qiongzhou Strait vary by about 45%, which may cause excessive erosions (Wang et al., 2013a). Thus, researches on sediment transport around artificial islands are popular in the recent decade in particular.
Han et al. (2007, 2009) constructed a series of physical models to simulate scours around coastal structures on a silt-sandy bed, and they coupled storm waves with spring tides for simulations. The results indicated that both storm waves and spring tides intensify the scours around an artificial island in terms of the erosion thickness and width, where rock armours are of great stability for protection under extreme events. Such phenomena are more evident for an artificial island which is close to the coast, where the littoral currents are accelerated due to reduced cross-sections between the island and the coast (Lin, 2017), and the littoral sediment transport is intensive simultaneously (Song, 2014). In addition, Zhong (2017) and Zou (2020) concentrated on the influences on an artificial island by a typhoon, and they found that artificial islands can hinder the typhoons and protect the coast from erosion, but for the exposed coast, beach nourishment is an effective approach for defence, as well as armour blocks (Li, 2015). Apart from marine conditions, river conditions are also significant to an artificial island at estuary (Liu et al., 2021; Ban and Wu, 2018). Sheng et al. (2016) and Zhang (2013) investigated the influences on Conch Island of a flood from the Tanghe Estuary, where the flood brings about massive sediment input and alter local morphological conditions in a short term. The construction of Conch Island affects the flow directions of flood and changes local sediment transport. Therefore, the extensions of Conch Island may alter local hydrodynamic conditions and lead a new trend of morphological evolution further.
As an international resort in the Bohai Sea of China, Conch Island is named after its layout and famous for the entertainment, aquatic sports and Yacht industry. With such comprehensive benefits, it plays a significant role in the development of local economy. However, poor management resulted in environment deterioration and biodiversity loss along the north-western shore of Conch Island. Therefore, the north-western shore is projected to be rebuilt by beach nourishment to improve its environment and attraction for a sustainable development. To investigate potential morphological responses of the projected beach along Conch Island, it is essential to focus on the floods from the Tanghe Estuary. A multi-coupled model is established and based on the data from recent surveys. The simulations are realized by MIKE 21 Flow Model (FM), where wave model, flow model, and sediment transport model are coupled together. Extreme events are designed under a storm in July 2021 for the investigation. Furthermore, influences of different components in extreme events are discussed. The present study aims to provide a feasible approach to estimate the morphological changes of the projected beach after a flood for effective management.
2 Materials and methods
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2.1 Research area
Conch Island is located at the Tanghe Estuary of Qinhuangdao, along the west coasts of the Bohai Sea (Fig. 1). The research area (Fig. 2) covers the Tanghe Estuary, Conch Island, Jinmeng Bay Beach, and Lotus Island mainly. The Tanghe River is 28.5 km in length and consists of two branches. The east branch (EB) is larger than the west branch (WB). A numerical model of Qinhuangdao nearshore area is established by MIKE 21 FM under Beijing Geodetic Coordinate System l954 (Fig. 3). The modelling area extends from Ledao Ocean Park in north to the Yanghe Estuary in south, with the length of 35.6 km along shore (NE−SW) and 16.5 km off shore (NW−SE). The total water area is approximately 587.4 km2, containing 22 942 nodes and 44 148 meshes. The grid length ranges from 4 m to 3 200 m (Fig. 3). The boundary conditions of open sea are provided by the Bohai Sea model, which has been introduced and validated in the previous research (Han et al., 2022).
The bathymetric data are based on a field survey in 2016 by Tianjin Exploration Centre of Marine Geology. The details about the survey can be referred to the previous research (Kuang et al., 2022). The bathymetry of Jinmeng Bay Beach is updated partially by the beach-profile survey with RTK (real-time kinematic) technique by the Eighth Geological Brigade of Hebei Geological Prospecting Bureau in August 2021 (Fig. 4).
Jinmeng Bay Beach was rebuilt by beach nourishment for berms and sandbars in 2010s, and the nourished beach profile can be treated as a smooth surface after the restoration (Xie et al., 2013). Figure 5 shows the observed data from a survey in August 2021, and the profiles are divided into three groups by their positions for analysis, where P1−P3 are close to Lotus Island; P4−P6 are between the two artificial islands; P7−P9 are close to Conch Island. As is shown in Fig. 5, the nearshore bed level of beaches covered by artificial islands (P1−P3 and P7−P9) are higher than those of open coasts (P4−P6), which means that artificial islands hinder landward actions from the open sea and defend the shore from erosion effectively. In addition, for open coasts, depositions occur on seaward sides of submerged sandbars and erosions occur on berms mainly (P4 and P5), where the sediment transport has a seaward trend. In cover areas of Lotus Island (P1 and P2), the generations of berms indicate that depositions dominate local morphological evolution. Particularly, the berms covered by Conch Island (P7−P9) are more evident due to its impermeable structure. Moreover, depositions occur within the distance from 400 m to 600 m, which results from the littoral sediment transport mainly. In a brief summary, in cover areas generated by Conch Island, where the projected beach is, deposition might be a main risk for the shore, because the littoral sediment transport dominates the morphological evolutions.
According to the project design by Qinghuangdao Qinzheng Real Estate Development Co., Ltd. (2021), the projected beach on the north-western shore of Conch Island extends 350 m in length. The intersecting profile (Dean, 1991) is utilized with a slope as 1:10. The designed berm under beach nourishment is 15 m in width with the top elevation as 2 m (1985 National Elevation Datum of China). The total volume of nourishment is 11.5 × 104 m3. Figure 6 shows bathymetries of the research area by the bare shore and the projected beach, respectively.
2.2 Methods
Hydrodynamic module and spectral wave module of MIKE 21 FM are coupled for simulations to include wave actions in real-world conditions. In addition, mud transport module is utilized to simulate the morphological impacts on the projected beach of a flood. Following governing equations can be referred to the manual of MIKE 21 FM, which is accessible on the official website of MIKE (https://www.mikepoweredbydhi.com/, accessed on August 15, 2023).
2.2.1 Hydrodynamic module
In this investigation, there is no source involved, so relative items are removed from the initial equations. The governing equations of hydrodynamic module are anchored in the integrations of continuity equation [Eq. (1)] and horizontal momentum equations [Eqs (2) and (3)] over depth as follows.
$ \frac{\partial h}{\partial t}+\frac{\partial h\overline{u}}{\partial x}+\frac{\partial h\overline{v}}{\partial y}=0 , $
$ \begin{split} \frac{\partial h\overline{u}}{\partial t}+\frac{\partial h{\overline{u}}^{2}}{\partial x}+\frac{\partial h\overline{u}^{\,}\overline{v}}{\partial y}=\,& f\overline{v}h-gh\frac{\partial \eta }{\partial x}-\frac{h}{{\rho }_{0}}\frac{\partial {p}_{{\mathrm{a}}}}{\partial x}+\frac{{\tau }_{{\mathrm{s}}x}}{{\rho }_{0}}-\frac{{\tau }_{{\mathrm{b}}x}}{{\rho }_{0}}-\\& \frac{1}{{\rho }_{0}}\left(\frac{\partial {s}_{xx}}{\partial x}+\frac{\partial {s}_{xy}}{\partial y}\right)+\frac{\partial }{\partial x}\left(h{T}_{xx}\right)+\\&\frac{\partial }{\partial y}\left(h{T}_{xy}\right) ,\\[-1pt]\end{split}$
$ \begin{split} \frac{\partial h\overline{v}}{\partial t}+\frac{\partial h\overline{u}^{\,} \overline{v}}{\partial x}+\frac{\partial h{\overline{v}}^{2}}{\partial y}= \,& -f\overline{u}h-gh\frac{\partial \eta }{\partial y}-\frac{h}{{\rho }_{0}}\frac{\partial {p}_{{\mathrm{a}}}}{\partial y}+\frac{{\tau }_{{\mathrm{s}}y}}{{\rho }_{0}}-\frac{{\tau }_{{\mathrm{b}}y}}{{\rho }_{0}}-\\&\frac{1}{{\rho }_{0}}\left(\frac{\partial {s}_{yx}}{\partial x}+\frac{\partial {s}_{yy}}{\partial y}\right)+\frac{\partial }{\partial x}\left(h{T}_{xy}\right)+\\&\frac{\partial }{\partial y}\left(h{T}_{yy}\right) ,\\[-1pt]\end{split}$
where $ h=\eta +d $ is the total water depth; $ \eta $ is the surface elevation and $ d $ is the still water depth; $ t $ is the time; $ \overline{u} $ and $ \overline{v} $ are the depth-averaged velocities; $ f=2{\Omega }\mathrm{sin}\phi $ is the Coriolis parameter; $ {\Omega } $ is the angular rate of revolution and $ \phi $ is the geographic latitude; $ g $ is the gravitational acceleration; $ {\rho }_{0} $ is the density of water; $ {p}_{{\mathrm{a}}} $ is the atmospheric pressure; $ ({\tau }_{{\mathrm{s}}x},{\tau }_{{\mathrm{s}}y}) $ and $ ({\tau }_{{\mathrm{b}}x},{\tau }_{{\mathrm{b}}y}) $ are the $ x $ and $ y $ components of the surface wind and bottom stresses; $ {s}_{xx} $, $ {s}_{xy} $, $ {s}_{yx} $, and $ {s}_{yy} $ are components of the radiation stress tensor; $ {T}_{xx} $, $ {T}_{xy} $, and $ {T}_{yy} $ are the lateral stresses, including viscous friction, turbulent friction and differential advection. The surface stress $ \overrightarrow{{\tau }_{{\mathrm{s}}}}=({\tau }_{{\mathrm{s}}x},{\tau }_{{\mathrm{s}}y}) $ is determined by the wind above the surface based on an empirical relation as follows:
$ \overrightarrow{{\tau }_{{\mathrm{s}}}}={\rho }_{{\mathrm{a}}}{c}_{{\mathrm{d}}}\left|\overrightarrow{{u}_{{\mathrm{w}}}}\right|\overrightarrow{{u}_{{\mathrm{w}}}} , $
where $ \overrightarrow{{u}_{{\mathrm{w}}}}=({u}_{{\mathrm{w}}},{v}_{{\mathrm{w}}}) $ is the wind speed 10 m above the sea surface; $ {\rho }_{{\mathrm{a}}} $ is the density of air. The hourly data of $ \overrightarrow{{u}_{{\mathrm{w}}}} $ are available on the European Centre for Medium-Range Weather Forecasts (ECMWF) [ERA5 hourly data on single levels from 1959 to present (copernicus.eu), accessed on August 15, 2023]. The drag coefficient $ {c}_{{\mathrm{d}}} $ in Eq. (4) can be calculated by the following empirical formula proposed by Wu (1980, 1994).
$ {c}_{{\mathrm{d}}}=\left\{\begin{array}{lc}{c}_{{\mathrm{a}}},& {w}_{10} < {w}_{{\mathrm{a}}},\\{c}_{{\mathrm{a}}}+\dfrac{{c}_{{\mathrm{b}}}-{c}_{{\mathrm{a}}}}{{w}_{{\mathrm{b}}}-{w}_{{\mathrm{a}}}}\left({w}_{10}-{w}_{{\mathrm{a}}}\right),& {w}_{{\mathrm{a}}}\leqslant {w}_{10} < {w}_{{\mathrm{b}}},\\{c}_{{\mathrm{b}}},& {w}_{10}\geqslant {w}_{{\mathrm{b}}},\end{array}\right. $
where $ {w}_{10} $ is the wind velocity 10 m above the sea surface; $ {c}_{{\mathrm{a}}} $, $ {c}_{{\mathrm{b}}} $, $ {w}_{{\mathrm{a}}} $, and $ {w}_{{\mathrm{b}}} $ are the empirical factors with the default values as ca = 1.255 × 10−3, cb = 2.425 × 10−3, wa = 7 m/s and wb = 25 m/s. The bottom stress $ \overrightarrow{{\tau }_{{\mathrm{b}}}}=({\tau }_{{\mathrm{b}}x},{\tau }_{{\mathrm{b}}y}) $ in Eqs (2) and (3) is determined by a quadratic friction law as follows:
$ \overrightarrow{{\tau }_{{\mathrm{b}}}}={\rho }_{0}{c}_{\mathrm{f}}\overrightarrow{{u}_{{\mathrm{b}}}}\left|\overrightarrow{{u}_{{\mathrm{b}}}}\right| , $
where $ \overrightarrow{{u}_{{\mathrm{b}}}}=(u,v) $ is the flow velocity above the bottom, which equals to the depth-average velocity for two-dimensional calculations; $ {c}_{{\mathrm{f}}} $ is the drag coefficient determined by the Manning number in this simulation.
$ {{{c}}}_{\mathrm{f}}=\frac{g}{{\left(M{h}^{1/6}\right)}^{2}} , $
where the Manning number $ M $ is generally given by 74 m1/3/s in the Bohai Sea (Kuang et al., 2022). Moreover, the radiation stress tensor in Eqs (2) and (3) dominates the coupling between hydrodynamic module and spectral wave module in MIKE 21 FM, and the components can be calculated as
$ \left\{\begin{array}{l}s_{xx}=E\left[\left(2n-1/2\right)-n\ \mathrm{sin}^2\ \theta\right], \\ s_{xy}=s_{yx}=E\ n\ \mathrm{cos}^2\ \theta, \\ s_{yy}=E\left[\left(n-1/2\right)+n\ \mathrm{sin}^2\ \theta\right],\end{array}\right. $
where $ E=\rho g {H}^{2}/8 $ is the wave energy and $ H $ is the wave height; $ n={c}_{{\mathrm{g}}}/c $ is the transfer rate; $ {c}_{{\mathrm{g}}} $ is the magnitude of the group velocity [Eq. (9)] and $ c $ is the phase velocity [Eq. (10)]; $ \theta $ is the wave direction.
$ {c}_{{\mathrm{g}}}=\frac{\partial \sigma }{\partial k}=\frac{1}{2}\left[1+\frac{2kh}{\mathrm{sinh}\left(2kh\right)}\right]\frac{\sigma }{k} , $
$ c=\frac{\sigma }{k} , $
where $ k $ is the magnitude of the wave number vector $ \overrightarrow{k} $; $ \sigma $ is the relative angular frequency. In addition, the lateral stresses in Eqs (2) and (3) can be estimated by an eddy viscosity formulation based on $ \overline{u} $ and $ \overline{v} $ as follows.
$ {T}_{xx}=2A\frac{\partial \overline{u}}{\partial x} , $
$ {T}_{xy}=A \left(\frac{\partial \overline{u}}{\partial y}+\frac{\partial \overline{v}}{\partial x}\right) , $
$ {T}_{yy}=2A\frac{\partial \overline{v}}{\partial y} , $
where $ A $ is the horizontal eddy viscosity, and the sub-grid scale eddy viscosity can be calculated by Eq. (14) given by Smagorinsky (1963).
$ A={c}_{{\mathrm{s}}}^{2}{l}^{2}\sqrt{2{S}_{ij}{S}_{ij}} , $
where $ {c}_{s} $ is a constant, which is set as 0.28 in this study; $ l $ is the characteristic length and the deformation rate $ {S}_{ij} $ is given by
$ {S}_{ij}=\frac{1}{2}\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right),\; i, j=1, 2. $
2.2.2 Spectral wave model
Spectral wave module is described by the transport equation for wave action density.
$ N=\frac{E}{\sigma } , $
where $ N(\sigma ,\theta ) $ is the wave action density; $ E(\sigma ,\theta ) $ is the energy density. In horizontal Cartesian co-ordinates, the conservation equation for wave action can be written as
$ \frac{\partial N}{\partial t}+\nabla \cdot \left(\overrightarrow{v}N\right)=\frac{S}{\sigma } , $
where $ N(\overrightarrow{x},\sigma ,\theta ,t) $ is the action density; $ \overrightarrow{x} = (x,y) $ is the Cartesian co-ordinates; $ \nabla $ is the four-dimensional differential operator; $ \overrightarrow{v}=({c}_{x},{c}_{y},{c}_{\sigma },{c}_{\theta }) $ is the propagation velocity of a wave group in the four-dimensional phase space; $ S $ is the source term for the energy balance equation. The four characteristic propagation speeds as follows:
$ \left({c}_{x},{c}_{y}\right)=\frac{{\mathrm{d}}\overrightarrow{x}}{{\mathrm{d}}t}={\overrightarrow{c_{{\mathrm{g}}}}}+\overrightarrow{U} , $
$ {c}_{\sigma }=\frac{{\mathrm{d}}\sigma }{{\mathrm{d}}t}=\frac{\partial \sigma }{\partial h}\left[\frac{\partial h}{\partial t}+\overrightarrow{U}\cdot {\nabla }_{\overrightarrow{x}}h\right]-{c}_{{\mathrm{g}}}\overrightarrow{k}\cdot \frac{\partial \overrightarrow{U}}{\partial s} , $
$ {c}_{\theta }=\frac{{\mathrm{d}}\theta }{{\mathrm{d}}t}=-\frac{1}{k}\left[\frac{\partial \sigma }{\partial h}\frac{\partial h}{\partial m}+\overrightarrow{k}\cdot \frac{\partial \overrightarrow{U}}{\partial m}\right] , $
where $ \overrightarrow{U}=(u,v) $ is the flow velocity; $ {\nabla }_{\overrightarrow{x}} $ is the two-dimensional differential operator in the $ \overrightarrow{x} $-space; $ s $ is the space co-ordinate in the wave direction $ \theta $; $ m $ is a co-ordinate perpendicular to $ s $. Furthermore, the energy source term $ S $ represents the superposition of source functions as
$ S={S}_{{\mathrm{in}}}+{S}_{{\mathrm{nl}}}+{S}_{{\mathrm{ds}}}+{S}_{{\mathrm{bot}}}+{S}_{{\mathrm{surf}}} , $
where $ {S}_{{\mathrm{in}}} $ is the generation of energy by wind; $ {S}_{{\mathrm{nl}}} $ is the wave energy transfer due to non-linear wave-wave interaction; $ {S}_{{\mathrm{ds}}} $ is the dissipation of wave energy due to white capping; $ {S}_{{\mathrm{bot}}} $ is the dissipation due to bottom friction; $ {S}_{{\mathrm{surf}}} $ is the dissipation of wave energy due to depth-induced breaking.
2.2.3 Mud transport module
Mud transport module is based on the advection-dispersion equation.
$ \frac{\partial h\overline{c}}{\partial t}+\frac{\partial hu\overline{c}}{\partial x}+\frac{\partial hv\overline{c}}{\partial y}=\frac{\partial }{\partial x}\left({D}_{x}\frac{\partial h\overline{c}}{\partial x}\right)+\frac{\partial }{\partial y}\left({D}_{y}\frac{\partial h\overline{c}}{\partial y}\right)-h{S}_{{\mathrm{ND}}} , $
where $ \overline{c} $ is depth averaged concentration; $ {D}_{x} $ and $ {D}_{y} $ are the dispersion coefficients; $ {S}_{{\mathrm{ND}}}={S}_{{\mathrm{D}}}-{S}_{{\mathrm{E}}} $ is the net deposition term; $ {S}_{{\mathrm{D}}} $ and $ {S}_{{\mathrm{E}}} $ are the deposition item and erosion item. For cohesive sediments, the deposition item can be calculated as Eq. (23) given by Krone (1962),
$ {S}_{{\mathrm{D}}}={w}_{{\mathrm{s}}}{c}_{{\mathrm{b}}}{p}_{{\mathrm{d}}} , $
where ${w}_{\mathrm{s}}$ is the settling velocity; ${c}_{\mathrm{b}}$ is the near bed concentration; ${p}_{\mathrm{d}}$ is the probability of deposition,
$ {p}_{{\mathrm{d}}}=1-\frac{{\tau }_{{\mathrm{b}}}}{{\tau }_{{\mathrm{cd}}}}{\tau }_{{\mathrm{b}}}\leqslant {\tau }_{{\mathrm{cd}}} , $
where $ {\tau }_{{\mathrm{b}}} $ is the bed shear stress; $ {\tau }_{{\mathrm{cd}}} $ is the critical bed shear stress for deposition. The near bed concentration is related to the depth averaged concentration (Teeter, 1986),
$ \beta =\frac{{c}_{\mathrm{b}}}{\overline{c}} , $
$ \beta =1+\frac{{P}_{{\mathrm{e}}}}{1.25+4.75{{p}_{{\mathrm{d}}}}^{2.5}} , $
$ {P}_{{\mathrm{e}}}=\frac{6{w}_{{\mathrm{s}}}}{\kappa {U}_{{\mathrm{f}}}} , $
where $ {P}_{{\mathrm{e}}} $ is the Peclet number; $ \kappa $ is Von Karman’s universal constant, $ \kappa =0.4 $; $ {U}_{{\mathrm{f}}}=\sqrt{{\tau }_{{\mathrm{b}}}/\rho } $ is the friction velocity. Meanwhile, for dense, consolidated bed the erosion is defined as
$ {S}_{{\mathrm{E}}}=G{\left(\frac{{\tau }_{{\mathrm{b}}}}{{\tau }_{{\mathrm{ce}}}}-1\right)}^{n},\;{\tau }_{{\mathrm{b}}} > {\tau }_{{\mathrm{ce}}} , $
where $G$ is the erodibility of bed; $ {\tau }_{{\mathrm{ce}}} $ is the critical bed shear stress for erosion; $ n $ is the power of erosion.
In MIKE 21 FM Mud transport module, fine sand fraction can be activated for simulation. The erosion item and the deposition item are given by
$ {S}_{{\mathrm{e}}}=\left(\frac{{\overline{c}}_{{\mathrm{e}}}-\overline{c}}{{t}_{{\mathrm{s}}}}\right),\;{\overline{c}}_{{\mathrm{e}}} > \overline{c} , $
$ {S}_{{\mathrm{d}}}=-\left(\frac{{\overline{c}}_{{\mathrm{e}}}-\overline{c}}{{t}_{{\mathrm{s}}}}\right),\;{\overline{c}}_{{\mathrm{e}}} < \overline{c} , $
where $ {\overline{c}}_{{\mathrm{e}}} $ is depth-averaged equilibrium concentration; $ \overline{c} $ is a compound concentration; $ {t}_{{\mathrm{s}}} $ is a time-scale
$ {t}_{{\mathrm{s}}}=\frac{{h}_{{\mathrm{s}}}}{{w}_{{\mathrm{s}}}} , $
where $ {h}_{{\mathrm{s}}} $ is the average water depth.
$ {\overline{c}}_{{\mathrm{e}}}=\frac{{q}_{{\mathrm{s}}}}{\overline{u}h} , $
$ {q}_{{\mathrm{s}}}={{\int }}^h_{ a} {c}_{{\mathrm{s}}}u\cdot {\mathrm{d}}z , $
where $ {q}_{{\mathrm{s}}} $ is the suspended load transport; $ \overline{u} $ is the depth averaged flow velocity; ${c}_{{\mathrm{s}}}$ and $ u $ are the sediment concentration and flow velocity at distance z from bed, respectively; $ a $ is the layer thickness, which equals to the equivalent roughness height.
2.3 Model setup
2.3.1 Sediment characteristics
According to previous researches (Sheng et al., 2016; Xie et al., 2013) and recent surveys on Jinmeng Bay Beach by utilization of laser particle size analysers in 2021. There are two main kinds of sediments in the research area, including silts and sands. The grain-sizes of silts range from 0.05 mm to 0.07 mm, while the grain-sizes of sands range between 0.15 mm and 0.23 mm. Thus, two sediment fractions are set for the present investigation with uniform grain-sizes, silt fraction ($ {d}_{50}=0.06\;\mathrm{m}\mathrm{m} $) and sand fraction ($ {d}_{50}=0.20\;\mathrm{m}\mathrm{m} $), respectively.
The grain-size of silts is larger than 0.03 mm, so the flocculation of silts can be neglected (Wang et al., 2013b). Sediment settling velocity $ {w}_{{\mathrm{s}}} $ can be calculated by Stokes’s formula [Eq. (34)] (Cheng, 1997).
$ {w}_{s}=\frac{1.65g{{d}_{50}}^{2}}{18\upsilon } , $
where $ g $ is gravitational acceleration, 9.81 m/s2; $ \upsilon $ is water viscosity, 1.01 × 10−6 m2/s; $ {d}_{50} $ is 50 percent fractile of grain-size of sediment. Settling velocity of sands ($ {d}_{50}=0.20\;\mathrm{m}\mathrm{m} $) is calculated as 0.036 m/s and that of flocculated silts ($ {d}_{50}=0.06\;\mathrm{m}\mathrm{m} $) is 0.0032 m/s. According to the empirical relation (Cao and Wang, 1994), the critical deposition shear stress $ {\tau }_{{\mathrm{cd}}} $ equals 4/9 of the critical erosion shear stress $ {\tau }_{{\mathrm{ce}}} $, and the critical erosion shear stress can be calculated by Eq. (35) given by Tang (1963).
$ {\tau }_{{\mathrm{ce}}}=\frac{1}{77.5}\left[3.2\left({\rho }_{{\mathrm{s}}}-\rho \right)g{d}_{50}+{\left(\frac{\sigma }{{\sigma }_{0}}\right)}^{10}\frac{C}{{d}_{50}}\right] , $
where $ {\rho }_{{\mathrm{s}}}=2.65\times {10}^{3}\;\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3} $ is the density of sediment grains; $ \rho $ is the density of water; $ \sigma /{\sigma }_{0} $ represents stability of volumetric weight, and it equals 1 for consolidated mud; $ C=2.9\times {10}^{-5}\;\text{kg/m} $ is a constant. Thus, the critical erosion shear stress of the silt ($ {d}_{50}=0.06\;\mathrm{m}\mathrm{m} $) is estimated by 0.065 N/m2, and its critical deposition shear stress is set as 0.029 N/m2. The critical erosion shear stress of the sand ($ {d}_{50}=0.20\;\mathrm{m}\mathrm{m} $) is estimated by 0.032 N/m2, and its critical deposition shear stress is set as 0.014 N/m2.
2.3.2 Bed layer characteristics
According to the detailed sedimentologic information by Wang (2014), two types of layers are set for the sea bed. The additional layers represent artificial sand beaches, covering Jinmeng Bay Beach and the projected beach, respectively, and the bed layer is 2 m in thickness. Table 1 shows the details of the layers.
In addition, the equivalent roughness height $ {k}_{{\mathrm{s}}} $ is estimated by
$ {k}_{{\mathrm{s}}}=2{d}_{50} , $
where $ {k}_{s} $ is set as 0.00012 m by grain-size of silts ($ {d}_{50}=0.06\;\mathrm{m}\mathrm{m} $).
2.3.3 Flood process
Sheng et al. (2016) introduced an approach to design the flood hydrograph of the Tanghe River. Same magnification method is utilized to design the flood, which is based on the recorded flood No. 980713 at Qinhuangdao Station. The maximum sediment input with the flood is referred to the records in Shihe Reservoir on July 29, 1991 as 0.16 kg/m3. This value matched the average annual sediment concentration at the Tanghe Estuary (Sheng et al., 2016).
Table 2 and Fig. 7 show the details of the designed flood process.
2.3.4 Scenarios
To investigate potential responses of the projected beach to a flood in extreme events, four scenarios are simulated under real-world conditions in July 2021 during a storm. Figure 8 shows peak wind vector field during the storm. Table 3 contains more information about the scenarios.
2.4 Validation
The wave model is validated by the observation at WS (Fig. 1) in June 2020. Figure 9 shows validations of significant wave height, mean wave period, and mean wave direction. The trends of simulated values match well with the observed data.
Both sediment concentration and beach profiles are validated for sediment transport model. The sediment concentration was collected at SS (Fig. 1) during October 18 to 19, 2016. The beach profiles for validation (Fig. 4) were measured in April 2022. Figures 10 and 11 show validations of sediment concentration and beach profiles, respectively. The initial bed levels in August 2021 are posted simultaneously, but the survey in 2021 extended much further (Fig. 5), so Fig. 11 shows the parts with the observation in 2022. As is shown in Fig. 11, Jinmeng Bay Beach is stable in terms of the morphology from August 2021 to April 2022.
The following skill model (Willmott, 1981) is used to evaluate the model performance based on validations of wave model and sediment transport model.
$ \mathrm{skill}=1-\frac{\displaystyle\sum_{i\ =\ 1}^j\left| {M}_{{\mathrm{s}}}-D\right|^2}{\displaystyle\sum_{i\ =\ 1}^j\left(\left|{M}_{{\mathrm{s}}}-\overline{D}\right|+\left|D-\overline{D}\right|\right)^2}, $
where ${M}_{{\mathrm{s}}} $ and $ D $ are the data from simulation and observation, respectively; $ \overline{D} $ is the average of observed data; $ j $ is the number of observed data. A skill value as 1.0 indicates a perfect performance of the model; 0.65−1.00 for excellent models; 0.50−0.65 for very good models; 0.20−0.50 for good models; below 0.20 for poor models. Evaluation results by skill values show in Table 4.
In Table 4, both wave model and sediment transport model are of good performances in the research area. Validations for Jinmeng Bay Beach profiles turn out to be excellent, which is important for following investigations on the morphological responses of the projected beach to a flood under extreme events.
3 Results
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3.1 Flow field
The designed flood process lasts 200 h (Fig. 7), and the peak discharge of flood occurs at 21 h. Figure 12 shows flow fields at typical moments by each scenario, including the peak flood (18 h), flood slack (21 h) and peak ebb (24 h). Figures 12a and b (excluding flood) illustrates that the hydrodynamic conditions are poor along the north-west shore of Conch Island, where the flow velocity is below 0.10 m/s generally. At the peak ebb (24 h), there is a tiny increase of the flow velocity along the target shore, because the projected beach reduces the cross-sections and accelerates the littoral currents. However, the influences on the littoral currents are limited under the weak tidal actions at the estuary.
According to Figs 12c and d (including flood), the flood dominates the hydrodynamic conditions along the north-west shore of Conch Island. The flood from EB is separated by Conch Island, where the main branch goes along the east shore of Conch Island, while the other branch turns towards Jinmeng Bay beach along the target shore. Meanwhile, the flood from WB is of a littoral trend with relatively low flow velocity. At the peak flood (18 h), the flow velocity along the east shore of Conch Island increases after the project (Fig. 12d), while the littoral branch of flood along the target shore turns weak. When the peak discharge of flood occurs, the flow velocity at the north corner of Conch Island decreases below 0.20 m/s after the project. It indicates that the projected beach restricts the flood for decreased cross-sections. At the peak ebb (24 h), the flood discharge is still large, so the flood reverses the initial current directions along the target shore. However, the littoral branch of flood is hindered by ebb tidal currents and wave-induced currents along Jinmeng Bay Beach. Under this circumstance, the ebb tidal currents and the littoral branch of flood are confluent between Lotus Island and Conch Island, and then turn to the open sea through the channel. In a brief summary, the flood dominates the hydrodynamic conditions at the estuary under weak tidal actions, and the projected beach hinders the flood towards the open sea.
3.2 Sediment concentration
Figure 13 shows distributions of mean sediment concentrations during the flood process. In Scenario 1 (Fig. 13a), when flood is excluded, the mean sediment concentrations maintain the initial value about 0.02 kg/m3 in general. According to local hydrodynamic characteristics, suspended sediments settle gradually with inadequate supplements at the estuary. Compared with EB, WB is faced with weaker actions for its limited scales. In this situation, the sediment concentration at WB is less than 0.008 kg/m3 particularly. After the construction of projected beach in Scenario 2 (Fig. 13b), the littoral tidal currents speed up and intensify local sediment transport along the projected beach, so the sediment concentrations are relatively higher at the estuary.
Figure 13c illustrates that the sediment input with flood generates a zone with high sediment concentration around Conch Island, and the maximum mean value is up to 0.035 kg/m3 inside the zone. Compared with Scenario 1, it is evident that the sediment input with flood plays an important role in local sediment transport. Such an increase in sediment concentration may result from two inducements. On the one hand, the intensive flood actions contribute to massive bed scours at the estuary, and then local sediment concentration rises considerably. On the other hand, after the peak discharge of flood, tides take over the dominations of local hydrodynamic conditions gradually, and then suspended sediments accumulate at the estuary for the weak tidal actions. In Scenario 4 (Fig. 13d), there is a great decrease in sediment concentration in the research area compared with that in Scenario 3. In details, the maximum value in the high-concentration zone around Conch Island is 0.028 kg/m3, where the decrease is up to 20%. Once the flood happens, the projected beach hinders the flood, and restricts the bed scours from the flood indirectly. Therefore, the target shore is faced with a lower risk of excessive accretion after the flood under the protection by beach nourishment.
3.3 Morphological changes
According to the distributions of mean sediment concentrations, the bed scours at the estuary are likely to cause additional suspended sediments, which ought to be verified by the morphological changes further. Considering that the flood process lasts 200 h, the final morphological changes at 200 h in the research area are posted in Fig. 14.
When the flood is excluded (Figs 14a and b), the erosions occur along the south and the east shores of Conch Island, where tidal currents are in relatively high velocities (Fig. 12), and the maximum erosion depth is within 0.01000 m. The deposition just occurs at the east end of projected beach in Scenario 2 (Fig. 14b), where the maximum deposition depth is 0.00004 m. When the flood happens (Figs 14c and d), the bed of the Tanghe Estuary suffers from flood-induced scours, and the maximum erosion depth in EB is about 0.04000 m. The morphological changes correspond with the sediment transports in the research area, that the estuary suffers more scours in Scenario 3 than that in Scenario 4. Although the flood enhances the erosions on the south and the east of Conch Island, the sediment transport by the littoral branch of flood is hindered by the projected beach effectively. The maximum deposition depth at the east end of projected beach is about 0.00003 m, which is close to the value in Scenario 2. Under such circumstances, the accretions result from the tidal currents rather than the flood. In fact, most suspended sediments transport to the open sea by the flood, and then the tidal currents with high sediment concentration contribute to accretions. In other words, the tidal currents can compensate a part of sediments for the loss from flood-induced scours at the estuary.
4 Discussion
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Simulations of previous scenarios (Scenarios 1−4) are based on the real-world conditions in July 2021. To simulate extreme events, the spring tides are included. Influences on the projected beach of the components in extreme events are further discussed. In addition, considering the constructions of rubber dams at the Tanghe Estuary, the risks of local bed scours rise during the flood process, that the maximum sediment input may increase. Therefore, more values of the maximum sediment inputs are taken into accounts, including 0.50 kg/m3, 1.00 kg/m3, and 2.00 kg/m3. Table 5 shows the details.
Figure 15 shows mean flow fields during the flood process for discussion. In Scenario 5 (Fig. 15a), the mean flow velocity at the estuary is in a low level (below 0.04 m/s). The variations of cross-sections at the north corner of Conch Island cause high flow velocity by about 0.18 m/s. Moreover, the sandbars along Jinmeng Bay Beach decelerate the littoral currents apparently. In Scenario 6 (Fig. 15b), the flood intensifies and dominates the hydrodynamic actions at the estuary, where the maximum mean flow velocity at the Tanghe Estuary increases to 0.25 m/s approximately. Meanwhile, the maximum mean flow velocity along the east side of Conch Island increases from 0.20 m/s to 0.23 m/s by 15%. Nevertheless, the landward storm winds have negative effects on the flood in Scenario 7 (Fig. 15c), and the maximum mean flow velocity at the Tanghe Estuary decreases to 0.23 m/s. Furthermore, the storm winds intensify the littoral currents. When the storm waves are included (Fig. 15d), wave-induced currents along Jinmeng Bay Beach are intensive, with the maximum mean flow velocity over 0.28 m/s. Meanwhile, the storm waves result in a tiny decrease on the mean flow velocities at the estuary, because the wave actions are hindered by Conch Island. The hydrodynamic characteristics along the projected beach are similar among Scenarios 6−8, which illustrates that storm winds and waves can barely affect the projected beach under the protections by Conch Island.
Figure 16 shows distributions of mean sediment concentrations during the extreme event. To show the differences between these scenarios, the representative patterns of Scenarios 6−8 are under the maximum sediment inputs as 2.00 kg/m3. In Scenario 5, the flood is excluded, so the sediment input is 0. According to Fig. 16a, the sediment concentrations maintain as the initial value (0.02 kg/m3) in Scenario 5. In Scenario 6 (Fig. 16b), the suspended sediments transport with flood to the open sea, and the high-concentration zone covers a considerable area. There are few cores with the maximum values as 0.28 kg/m3 inside the zone, and the maximum value at the estuary is up to 0.20 kg/m3. Simultaneously, the suspended sediments can barely settle under intensive tidal actions, so the spring tides may extend the high-concentration zone further. Once the storm is included, the flood actions are weakened by landward winds (Fig. 16c). The maximum sediment concentration around Conch Island declines to 0.21 kg/m3 by 25%, and the maximum value at the estuary decreases to 0.17 kg/m3 by 15%. When the storm waves are included (Fig. 16d), the flood can hardly reach Lotus Island due to the wave-induced littoral currents, so the high-concentration zone mainly is around Conch Island with the maximum value as 0.15 kg/m3. Compared with Scenario 6, the maximum sediment concentration decreases by about 46% under the combined actions of storm winds and waves in Scenario 8. According to Fig. 16, the maximum mean sediment concentrations along the projected beach in Scenarios 6−8 are collected for following discussions. Table 6 shows maximum mean sediment concentrations along the projected beach in Scenarios 6−8.
As is shown in Table 6, the storm winds and waves can reduce the maximum mean sediment concentration along the projected beach by restricting flood actions. Compared with Scenario 6, the storm winds contribute to a decrease by 21% in Scenario 7, and with the combined actions of storm winds and waves, the decrease is up to 38% in Scenario 8. During the collections, the maximum mean sediment concentrations generally occur at the west end of the projected beach. Therefore, the west end of projected beach is selected as a representative position for following discussions on morphological changes.
At the end of the flood process (200 h), the deposition depths at the west end of projected beach in Scenarios 5−8 are collected. Details are as follows in Table 7. Based on the values, a relationship between the deposition depths and the maximum sediment inputs with the flood is established (Fig. 17), where Scenario 5 acts as a reference for Scenarios 6−8.
There is a quadratic polynomial relationship between the deposition depths and the maximum sediment inputs with flood in Fig. 17. The coefficient of determination, R2, is up to 1.0 for each fitting in Scenarios 6−8. In the equations, the constant item, 0.0000003, represents a common condition in Scenario 5, which indicates that the position is in a deposition state even without the flood. In the extreme event, the deposition depths are related to the flood actions, because the sediment inputs with flood are main sources. Under the same sediment input, once the storm winds and waves are included, the deposition depths decrease with the weakened flood actions. With such relationships, it is accessible to estimate the deposition depths on the projected beach after the flood process in extreme events.
5 Conclusions
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The morphological responses of the projected beach on the north-west shore of Conch Island to a flood in extreme events are investigated by field observations and numerical modelling. Based on the recent surveys on Jinmeng Bay Beach, a multi-coupled model is established, which covers the Tanghe Estuary, Conch Island, Lotus Island and Jinmeng Bay Beach. Qualitative analysis and quantitative analysis are utilized to investigations on local hydrodynamic characteristics and sediment transports. Then the impacts on the projected beach of the components in extreme events are discussed, including the flood, spring tides, storm winds, storm waves and sediment inputs. The findings are as follows.
(1) According to the field observations of Jinmeng Bay Beach, artificial islands have positive effects on coasts by hindering landward waves. Meanwhile, the structures rise the risk of excessive deposition on the projected beach.
(2) Flood dominates the hydrodynamic conditions at the estuary under weak tidal actions. Moreover, it brings massive sediment inputs and additional sediments from flood-induced scours. However, the accretions along the target shore result from the tidal currents with high sediment concentration rather than the flood.
(3) The projected beach mitigates the flood actions and restricts the flood-induced scours indirectly. Therefore, it contributes to a decrease by about 20% of the maximum mean sediment concentration during the flood process.
(4) The storm winds decelerate the flood, and decrease the maximum mean sediment concentration along the projected beach by 21%. In addition, the wave-induced currents restrict the littoral branch of flood, and the decrease of the maximum mean sediment concentration along the projected beach reaches 38% under the combined actions of storm winds and waves.
(5) A quadratic polynomial relationship between the deposition depths and the maximum sediment inputs with flood is established to estimate the morphological changes of the projected beach after the flood process in extreme events for future managements.
In this study, the designed flood process is based on the flood and the sediment concentration from records. With climate changes, the estuarine floods are of uncertainty recently. Therefore, for sustainable managements, it is essential to monitor the hydrodynamic variations in the Tanghe River, and the sediment characteristics at the estuary.
Funding
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  • The National Key Research and Development Program of China under contract No. 2022YFC3106205; the National Natural Science Foundation of China under contract Nos 41976159 and 41776098.
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Appendix
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Year 2024 volume 43 Issue 7
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doi: 10.1007/s13131-023-2184-8
  • Receive Date：2023-10-26
  • Online Date：2025-11-19
  • Published：2024-07-25
Article Data
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History
  • Received：2023-10-26
  • Accepted：2024-01-18
Funding
The National Key Research and Development Program of China under contract No. 2022YFC3106205; the National Natural Science Foundation of China under contract Nos 41976159 and 41776098.
Affiliations
    1 College of Civil Engineering, Tongji University, Shanghai 200082, China
    2 The Eighth Geological Brigade, Hebei Geological and Mineral Exploration Development Bureau, Qinhuangdao 066001, China
    3 Marine Ecological Restoration and Smart Ocean Engineering Research Center of Hebei Province, Qinhuangdao 066001, China

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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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