XIE Ming-xiao

Key Laboratory of Engineering Sediment of Ministry of Transport, Tianjin Research Institute for Water Transport Engineering, M.O.T., Tianjin 300456, China, E-mail: xiemx@tiwte.ac.cn

ZHANG Wei

College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China

NUMERICAL STUDY ON THE THREE-DIMENSIONAL CHARACTERISTICS OF THE TIDAL CURRENT AROUND HARBOR ENTRANCE*

XIE Ming-xiao

Key Laboratory of Engineering Sediment of Ministry of Transport, Tianjin Research Institute for Water Transport Engineering, M.O.T., Tianjin 300456, China, E-mail: xiemx@tiwte.ac.cn

ZHANG Wei

College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China

(Received May 29, 2010, Revised July 25, 2010)

A three-dimensional (3-D) numerical model is established to investigate the tidal current motion characteristics around the harbor entrance. Computational approaches consist of the finite difference method, time-splitting technique, C-grid, and a high-order turbulence closure model. The Ocean General Circulation Model (OGCM) inundation scheme is incorporated in the model. An engineering application, Lianyungang Harbor, China, is used as a real-life case. The model is validated by showing that the simulated results agree well with the field data. In the approach channel, the tidal current shows a deflection effect especially in the bottom layer. As for Lianyungang Harbor, a jet flow forms at the tip of the northern breakwater, which drives a circulation flow at the inner side of the harbor entrance. In the vertical, the flow is significantly stratified at the entrance section within the channel, where the flow direction varies between layers and the speed distribution is quite uniform. These 3-D features become less evident to the offshore. Additionally, the sensitivity analysis shows that the flow deflection is related to the channel depth. Simulation results also imply that the siltation rate at the entrance section of the approach channel tends to be more uniform by the 3-D flow motion feature, and could be more significant with the increase of the channel depth.

3-D model, harbor entrance, OGCM inundation scheme, stratification features

1. Introduction

An approach channel with double guard breakwaters is a common form of the planar layouts of sea harbor entrances. The main function of the breakwaters is to block the waves from propagating into the inner berths, and also to cut the alongshore sediment transport, which would reduce the siltation rate in the approach channel. The construction of the harbor entrance changes the local motion characteristics of the tidal current, especially a jet flow usually forms around the breakwater tip, bringing about a “cross flow” in the approach channel, which would directly affect the navigation safety of shipping vehicles. The magnitude of the cross flow is a key issue when designing the channel width as well as the entrance itself[1]. Additionally, a circulation flow often appears in the entrance, and this flow could enhance the siltation in the approach channel. Thus, a comprehensive investigation of the flow motion features around the harbor entrance is desirable.

In a numerical simulation, complex topographies and various coastal processes can be considered, such as the tidal current, waves, sediment transport, temperature/salinity, storm surge, hence it becomes an effective tool in basic researches as well as in engineering applications in recent years. The horizontal scale is much larger than the vertical scale for coastal regions, thus in most cases, the depth-integrated (2DH) models are adequate to investigate the environmental impact of the engineering structures, as reported widely in literature[2-5].

However, with the fast development of sea harbors in China nowadays, many approach channels have to be dredged directly from very shallow shoals(e.g., Lianyungang Harbor), hence the local bathymetry transits violently around the harbor entrance. The tidal current flows into the channel from shoals nearby, and with a sharp increase of the water depth, the flow motion shows conspicuous stratification features[5]. The 2DH models fail to describe these processes adequately, and a more sophisticated 3-D model is necessary.

The development and application of the 3-D numerical models are popular in recent years. With regard to the 3-D modeling, under different basic assumptions, numerical schemes, and grid systems, a considerable number of software (e.g., Delft3D, MIKE3, RMA10) and coastal ocean circulation models are available (e.g., POM, ECOMSED, ROMS, FVCOM) and are shown to be effective in practical engineering cases, e.g. the hydrodynamics, sediment transport, and temperature/salinity circulation[6-11].

In this article, a 3-D hydrodynamic model is established to investigate the tidal current flow characteristics around the harbor entrance. The numerical model was applied to a real engineering case, Lianyungang Harbor, China, by which to validate the model. Further discussions and relevant sensitivity analysis are also made.

2. Model description

2.1 Governing equations

The primitive governing equations are a phase-averaged Reynolds approximation of the original Navier-Stokes equations. The classical hydrostatic assumption is applied for the vertical momentum expression. Rectangular grids are used for the horizontal discretization, and the terrain-following sigma coordinate is adopted in the vertical. The ultimate governing equations are Eq.(1) through Eq.(3). Note that in order to help the post-processing, an additional equation is used to transform the vertical velocity from sigma to Cartesian coordinate systems (see Eq.(4)).

Continuity equation:

where σ is the vertical coordinate, x and y are the horizontal coordinates, t is time, U and V are horizontal velocity components, respectively, η is the free surface, ω and W are the vertical velocity component in sigma and Cartesian coordinates, respectively, D is the total depth, f is Coriolis factor, g is the gravity acceleration, KMis the vertical viscosity coefficient, which is solved by using the Mellor-Yamada turbulence closure model, AMis the vertical viscosity coefficient following the Smagorinsky formula.

2.2 Boundary conditions

The free surface boundary is controlled by the wind stress

where0xτ and0yτ are the wind stress components in x and y directions, respectively, ρ is the sea water density. If no wind is given as the input,0xτ and0yτ are set to zero.

The bottom boundary is controlled by the bed friction

where τbxand τbyare the bed friction components in x and y directions, respectively, CDis the drag coefficient, κ=0.4 is the von Karman constant, zbis the distance of the grid point nearest the bottom, z0is the roughness height.

The open boundary conditions are

in which1Ω represents the open boundary, the superscript ∗ expresses a given value (either the measured value or the analyzed value).

The closed boundary condition is

in which2Ω represents the closed boundary, n expresses the normal unit vector.

2.3 Initial conditions

The initial conditions are

where the subscript 0 expresses a given value (the measured value or the analyzed value).

2.4 Solution technique

The finite difference method with rectangular grids is adopted for solving the governing equations. In numerical simulations, the time-splitting technique proves to be an effective approach, and is successfully incorporated in most popular models (e.g., POM, ECOMSED, FVCOM). Hence, this method is also applied in this article, with the external mode providing the 2-D variables as η,U and V, while the internal mode providing the 3-D stratified velocities U(σ) and V(σ). For time stepping, the horizontal terms are treated explicitly and the vertical terms are treated implicitly using the “double-sweep”scheme. Variables are arranged using the staggered C-grid system.

2.5 Inundation scheme

The inundation scheme (also known as the wet/dry or movable boundary scheme) is very important for modeling the hydrodynamics within the inter-tidal zone. Based on different assumptions, many theories were developed to incorporate this scheme. However, most of the historical schemes focused on the 2-D models, without properly taking account of the 3-D conditions.

In the 2-D external mode, the inundation scheme reads Eq.(16) to Eq.(21):

In the 3-D internal mode, the inundation scheme follows Eq.(22) and Eq.(23):

The subscripts, ,,ijk represent ,,xyσ respectively.

3. Study site

Lianyungang harbor locates at the eastern coast of Jiangsu Province, and its geographical coordinates are (34o44'32˝, 199o27'28˝). The map and the bathymetry are shown in Fig.1. Note that the depth contours are drawn according to the Mean Sea Level (MSL).

The tide pattern is semidiurnal with a mean tidal range of 3.33 m. The dominant tidal constituent for Lianyungang Harbor is M2. The mean flood duration is 5 h 38 min, and the mean ebb duration is 6 h

48 min. Referring to the field survey performed in 2005-09, the speed of the flooding current is between 0.36 m/s - 0.87 m/s and the ebb current speed is between 0.37 m/s - 0.79m/s. The tidal current is bi-directional in the nearshore (approximately parallelto the shoreline), and becomes rotational towards the offshore.

4. Model validation

The tide levels for open boundaries are provided by a 2DH regional tidal current propagation numerical model of Eastern China Sea, which incorporates eight major tidal constituents (M2, S2, N2, K2, K1, O1, Q1, and P1). As for model validation, the calibration process was made based on the field data measured in 2005-09, and the verification was made using data from 2004-07. Due to limited space here, we only give results for several stations.

Rectangular grids are used for the horizontal discretization with a spacing of 150 m in the offshore area, which is refined to 50 m near the entrance. This gird resolution is adequate to describe the channel boundary and its side slope. As for the vertical segmentation, the water depth is divided into 6 sigma layers. The time step is set to 2.0 s for the external mode, and 18.0 s for the internal mode. The horizontal eddy viscosity parameter Csis calibrated to 0.20, which is in the same range as the recommended value (0.10 - 0.25). The bed roughness height is set as z0=0.0014m , which is consistent with what in literature.

Figure 4 compares the measured and simulated tide levels at Oil Port and Coal Port (see Fig.2), and stratified velocities/directions in both surface and bottom layers at stations A0402 and C0401 (see Fig.2). The results show that the simulated values are in a satisfactory agreement with the observed ones both in magnitudes or in phases.

When modeling the current motion features in the approach channel, one may doubt about the validity of the hydrostatic assumption and the terrain-following coordinate technique. Actually, these techniques do lead to potential errors especially within the channel and on its side slope. However, although the depth difference between the channel and the nearby shoals may lead to a great vertical acceleration. But theoretically, its value is very small, as compared to the gravity, therefore, it would not affect the integral flow structure in the channel.

5. Characteristics of the tidal current motion around harbor entrance

5.1 Horizontal features

In the following discussions, the spring tide during 2004-07-01 to 2004-07-03 is selected as the representative tidal cycle. The tidal current vectors of both surface and bottom layers are illustrated in Fig.5 and Fig.6, which indicate that the tidal current is fully rotational in the offshore and gradually becomes bi-directional onshore.

Noted that in the approach channel, the long-axis of the current ellipses tends to arrange along the channel. This tendency is more obvious in the bottom layer (see Fig.6), where the current directions are almost along the channel. This phenomenon is actually due to the flow inertia differences between vertical layers. The current in the surface layer directly enters the channel from nearby shoals with a large inertia, so the deflection effect is weak, but the current in the bottom layer is restricted by the bed friction and channel boundaries, and could not rotate freely, therefore, is compelled to deflect to the channel trend.

The jet flow appears at the tip of the northern breakwater, and its speed is large in the upper layer, probably exceeding 1.0 m/s. During the flooding process, the jet flow forms a strong cross-flow in the channel. However, the jet flow does not exist at the southern breakwater tip during ebbing. It is due to the fact that the direction of the flooding current is approximately normal to the northern breakwater, thus the flow energy is mainly concentrated at the tip, while the direction of the southern breakwater is parallel to the ebb flow.

The circulation flow is a common flow pattern within the inner entrance, which would generate an intensive siltation in the channel and harbor basins. Figs.7 and 8 show the flow fields of the maximum circulation at the time of 2004-07-02 4:00, which is the exact time when the jet flow generated by the northern breakwater reaches its largest value, and atthe same time, the flow is slack at the inner entrance. Therefore, the near-quiescence flow inside the entrance is driven by the strong inertia of the jet flow outside the entrance, which results in the circulation. According to Figs.7 and 8, one may also see that the circulation area in the surface layer is greater than that in the bottom layer.

5.2 Vertical features

In order to reveal the vertical features of the flow motion around the entrance more clearly, a schematic diagram of the flow field at the time of 2004-06-02 4:00 is shown in Fig.9. At that time, the jet flow generated by the northern breakwater reaches its maximum, while the current direction in the surface layer is approximately perpendicular to the outer channel. To facilitate discussions, three observation sections (S1- S3) including nine points are marked (see Fig.2).

From the left panel of Fig.9, the tidal current in the approach channel sees an obvious stratification feature. Take point S1#B as an example, the current direction in the surface layer points to the shoal (although obliquely), but in the bottom layer the current direction is along the channel. But for the shallow shoals of both sides, the stratification feature does not manifest, or at least is not significant. Additionally, the right panel of Fig.9 also shows that the gradient of the vertical velocity in the channel is relatively small compared to that on shallow shoals.

Generally, the 3-D features are more significant near the entrance, and gradually become weaker away from the entrance. That is because both the bed topography and the land boundary are more complicated around the entrance. To the offshore, as the bathymetry becomes smoother, the flow motion shows mainly 2-D features. For instance, at section S3# the stratification can hardly be distinguished even in the channel.

5.3 Sensitivity of the channel depth

Based on the discussions in the above sections, the stratification in the approach channel is related with the violent depth variation between the channel and nearby shoals. Actually, both laboratory experiments and numerical simulations show that the depth difference is a key factor that affects the flow structure. In order to further investigate its sensitivity, we simply dredge the approach channel in the model domain, to simulate another two cases: channel bottom elevation Hb=−16.5m (corresponding to 150 000DWT) and Hb=−11.5m (corresponding to 70 000DWT), the other conditions remain unchanged.

To save space, the simulation result of the case of Hb=−16.5m is not presented here. In Fig.10 and Fig.11, both the surface and bottom current elliptic vectors for the case of Hb=−11.5m are shown.

Comparing them with Figs.6 and 7 (Hb=−22.5m ), the following observations can be made:

(1) Generally, dredging of the channel does not alter the flow field in the large scale. The differences of current motions are mainly confined in a narrow area, e.g., within the approach channel.

(3) The stratification and the deflection effect are more significant for a deeper channel. Comparing the case of Hb=−22.5m (Figs.6 and 7) and the case of Hb=−11.5m (Figs.10 and 11), it is shown that the flow within the channel is more rotational for the case of Hb=−11.5m.

Additionally, note that for the bottom layer, the long-axis of current ellipses for the case of Hb=−11.5m is shorter than that for the case of Hb=−22.5m , which indicates that the maximum speed of the bottom current actually increases with the depth, which is just contradictory to the depth-averaged condition. This phenomenon affects the siltation feature in the approach channel, and can only be described by a 3-D model.

5.4 Potential impact on siltation

Experiences show that the maximum siltation in the approach channel takes place in the entrance section of the channel. Actually, the essence of erosion/deposition is the exchange of sediment fluxes at the bottom. To calculate the deposition, the formula of D=PSbωsis universally applied, where D is the deposition flux, P is the deposition probability, Sbis the sediment concentration at the water-bed interface, ωsis the settling velocity, which is also related to Sb.

Based on the above expression, the siltation rate in the approach channel is more closely related to the bottom sediment transport feature. Furthermore, it is indicated that the bottom flow motion feature makes the main contribution to the siltation. As seen from Figs.5 and 6, although the tidal current motion is mainly rotational in the Lianyungang area, the flow at the bottom layer within the channel is strongly bi-directional. This feature implies that the sediments settled to the bottom would be transported along the channel, which makes the channel siltation at the entrance section more uniform. Additionally, because the deflection effect becomes more significant with the increase of the channel depth, this “smoothening effect” tends to be more significant in a deeper channel. It should be noted that this effect could not be well described by the 2DH models.

6. Conclusions

(1) A 3-D hydrodynamic model is set up to investigate the current flow motion features around the harbor entrance. Numerical techniques include the finite difference method, time-splitting, C-grid, and a high-order turbulence closure model. Additionally, a 3-D OGCM inundation scheme is also incorporated in the model.

(2) An engineering application, Lianyungang Harbor, China, is used as a case study. The simulated tide level and the stratified current speed/direction are in good agreement with field data, which validates the model.

(3) The deflection effect takes place in the deep approach channel, especially in the bottom layer, which means that the long-axis of current ellipses deflects to the channel trend. As for Lianyungang Harbor, a jet flow would form at the tip of the northern breakwater, which then induces a circulation flow at the inner side of the harbor entrance.

(4) The current flow is significantly stratified at the entrance section within the approach channel, where the flow directions vary between vertical layers and the vertical speed gradient is small. Away from the harbor entrance, the stratification weakens.

(5) The deflection effect in the channel is sensitive to the channel depth. With the increase of the depth, this effect becomes more significant. Furthermore, the current speed in the bottom layer is greater for a deeper channel.

(6) Because the flow motion at the bottom layer in the approach channel is nearly bi-directional, thus the potential siltation rate distribution at the entrance section of the channel tends to be smoothened, and this feature would be more significant as the channel deepens.

Acknowledgement

This work was supported by the Central Public Institute Foundation of Tianjin Research Institute for Water Transport Engineering, M.O.T. (Grant No. TKS100102).

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10.1016/S1001-6058(09)60125-6

* Biography: XIE Ming-xiao (1982-), Male, Ph. D.