THREE-DIMENSIONAL FLOW-SALINITY-SEDIMENT  SIMULATIONS
 OF THE PEARL RIVER ESTUARY

 

 

Li Mengguo1 , Cai Dongming2 and Xu Hongming1

1Tianjin Research Institute of Water Transport Engineering, Tanggu,Tianjin, 300456, China

2Ocean Weather Center, Dalian Naval Academy, Dalian 116018,China

1Tel: +86 22 25707168-382, Fax: +86 22 25795125, E-mail: limengguo@sina.com

 

 

Abstract: By using -coordinate transformation technique, a three-dimensional (3-D) tidal flow governing equations, 3-D convection-diffusion equations of salinity and suspended sediment in the ( ) coordinate system are transformed into the equations in the ( ) coordinate system, which are solved discretely by using the finite difference method. The water level is solved with the direction integrated continuity equation, while the vertical structures of the flow velocity, salinity and sediment are solved respectively by the momentum equations, convection-diffusion equations of salinity and suspended sediment, thus, a 3-D mathematical model of flow, salinity and sediment is set up. In the flow model, the mean flow velocity on the vertical can be used as the open boundary conditions. With this model, the flow field, salinity field and sediment field during the dry and flood seasons in  the Pearl River estuary are numerically simulated, where the topography and coastal lines are complicated with multiple entrances and many islands. Comparing the results of the simulations to the measured data, they are in fair agreement with each other. On the basis of the simulations, the plane and spatial structural features of the flow field, salinity field and sediment field in the Pearl River estuary are analyzed.

 

Keywords: flow, salinity, sediment, numerical simulation, three dimension, the Pearl River estuary

1  INTRODUCTION

The Pearl River estuary is the only entrance and exit for the Port of Guangzhou. The Port of Shenzhen is located on its east coast. The existence and development of the two ports have been playing a tremendous role in the economic development in the Delta of the Pearl River. The constant development of the economy requires the ports to develop continuously. The development in the ports involves a series of problems, such as plane planning of the ports, selection of navigation channels, dredging and maintenance of navigation channels. The prerequisite and the basis for the solution of these problems are the full understanding of the hydrodynamic and sediment features of the Pearl River estuary. The basic features of the estuary are that the sea area is vast with many entrances and exits, including four rivers in the northwest flowing into the estuary, there are many islands in the estuary, the topography is irregular, and the flow pattern is complicated with different tidal phases in the upstream and the downstream. A 3-D mathematical model of flow, salinity and sediment is presented in the paper, which has been used to simulate numerically the flow field, salinity field and sediment field in the Pearl River estuary. The purpose for establishing such a model is to understand the characteristics of their plane distribution and spatial structure so as to provide scientific basis for the planning and construction of ports and navigation channels in the estuary and to provide boundary conditions for local mathematical models such as a mathematical model for sediment siltation in navigation channels.

In the 3-D mathematical model of flow-salinity-sediment, the simulation of 3-D tidal flow is the hinge and basis. A lot of research has been done and quite a number of methods have been developed for the mathematical models of 3-D tidal flow, out of which the method of coordinate transformation is more effective[1]. The 3-D mathematical model of flow-salinity-sediment presented in this paper is established with the technique of vertical coordinate transformation together with the finite difference method. For the equations in the new coordinate system, the water level is solved with the vertically-integrated continuity equation, while the vertical structures of the flow velocity, salinity and sediment are solved respectively by the momentum equations, convection-diffusion equations of salinity and sediment. In these operations, rectangular grids in horizontal direction and equidistant-layer division in vertical direction are used. As the vertically-integrated continuity equation is used to solve the water level, the mean velocity on the vertical can be used as the open boundary conditions, thus greatly facilitating the numerical solution of the flow field and conveniently facilitating the coupled solution of 2-D and 3-D models.

The 3-D model as developed in this paper has been used to numerically simulate the 3-D flow fields, salinity fields and sediment fields in the Pearl River estuary in dry and flood seasons.

2  MATHEMATICAL MODEL

2.1  Basic equations and definite conditions

2.1.1  Basic equations in (x, y, z) coordinate system

The basic equations for the 3-D mathematical model of flow, salinity and sediment include the continuity and momentum equations of flow, the convection-diffusion equations of salinity and sediment. In the right-handed Cartesian coordinate system (x, y, z) of f plane, the basic equations are as follows.

Continuity equation:

                                                      (1)

Momentum equations:

                                (2)

                            (3)

                                                         (4)

Convection-diffusion equation of salinity:

                                    (5)

Convection-diffusion equation of sediment:

                              (6)

In equations (1) through (6), x, y and z are the coordinates in the Cartesian coordinate system, in which axis z is vertically upwards and the origin of coordinate is located at the still sea surface; u, v and w are the components of velocity in the direction of x, y and z respectively; P is the hydrostatic pressure; is water density; g is acceleration due to gravity; is setting velocity of sediment in still water; S and C are the salinity and the sediment content respectively in the water; , and are eddy viscosity coefficients of water in the direction of x, y and z respectively; , and are the diffusion coefficients of salinity in the direction of x, y and z respectively; , and are diffusion coefficients of sediment in the direction of x, y and z respectively; t is time; and f is the Coriolis parameter. Equation (4) is the hydrostatic pressure equation, which is widely used in estuarine and coastal engineering, assuming that the water mass vertically satisfies the hypothesis or approximation of the hydrostatic pressure conditions[1].

2.1.2  Basic equations in (x, y, ) coordinate system

The coordinate transformation of , which is , is introduced, and after the transformation, the basic equations in the (x, y, ) coordinate system become as follows.

                                                                              (7)

                                 (8)

                                 (9)

                                       (10)

                                 (11)

                                                (12)

In the equations (7) through (12), is the water surface displacement relative to the x, y plane; H is the actual water depth, H = h + ; h is the distance from the sea bed to the x, y plane, i.e. the still water depth. It can be known from the expression of that, z = and = 0 at the sea surface while z = –h and = –1 at the sea bed, hence, both the sea surface and the sea bed become the coordinate planes in the (x, y, ) coordinate system, making range between –1 and 0, which becomes a new vertical coordinate. W is the component of vertical velocity in the (x, y, ) coordinate system and is related to w, the component of vertical velocity in the (x, y, z) coordinate system, by the following expression.

                                     (13)

Where, and  are the average values of the components of velocity in the x, y directions respectively along the water depth, which are  and .

Equations (7) through (13) are the basic equations of the 3-D mathematical model for flow, salinity and sediment as presented in the paper. It can be known from equation (7) that the open boundary conditions of flow may adopt the mean velocity on the vertical, which can greatly facilitate the actual calculation. Equations (8) through (11) are the equations of conservative type of u, v, S and C respectively, which are more accurate when discretizations are made with the finite difference method[2].

2.1.3  Definite conditions

The definite conditions in (x, y, ) coordinate system are as follows.

(1) Boundary conditions of the water surface:

                                    (14)

in which, and  are the components of wind stress in the  and  directions respectively.

(2) Boundary condition of the sea bed:

                                           (15)

in which, , and  are the critical shear stress of settlement, critical shear stress of scour and erosion constant respectively, and  and  are the components of bed friction vector in the x and y directions respectively,

                                                  (16)

in which,  is the Chezy coefficient,  ;  is the Manning roughness coefficient; and, and are the values of  and  near the seabed respectively.

(3) Shore boundary conditions

The component of velocity in the normal direction of the shore boundary is zero and the derivatives of  and C along the outer normal are also zero.

(4) Open(water-water) boundary conditions

The water level or the component of velocity, ,  or , are given. When  and  flow out of the calculation domain, we have

                                           (17)

When S and C flow into the calculation domain, we have

                                                                   (18)

where,  and  are known values; is the velocity vector of flow; and  is the unit vector in the exterior normal direction of the water boundary.

2.2  Numerical method

Equations (7) through (13) are discretely solved with simple finite difference method. In the operation, equidistant-layer division is used in the vertical and rectangular grids are used in the horizontal. All the variables are arranged on the same nodes, , and , of which,  and are the horizontal nodes while  is the th layer. The forward difference is adopted for the time derivatives. The explicit central difference is adopted for the horizontal spatial derivatives, and for equations (10) and (11), a upwind scheme is adopted for the horizontal convective terms. The implicit central difference is adopted for the spatial derivative in direction. After the equations are sorted out, an explicit difference equation for solving is obtained from the discrete result of equation (7); a set of tri-diagonal equations for vertically solving and are obtained respectively from the discrete results of equations (8) through (11); and the explicit difference equations for solving  and  are obtained respectively from the discrete results of equations (12) and (13). With these equations, the simulation calculation of any sea area can be carried out in combination with the definite conditions. References [2] and [3] may be referred to for the details about the difference discretizations and the difference equations.

3  NUMERICAL SIMULATIONS AND ANALYSES

3.1  Numerical simulations

The sea area to be numerically simulated is an area from Humen to Zhuhai-Lantau Island cross-section, which is about 70 km from the north to the south and about 50 km from the east to the west. There are six open boundaries in the simulated area, including Humen, Jiaomen, Hengmen, Hongqili, Hong Kong waterway and Zhuhai-Lantau Island cross-section, as shown in Figure 1. Horizontally, the domain of calculation is divided by square grids with spatial step size being x = y = 320 m and 17903 computational grid nodes. Vertically, the domain of calculation is divided into 11 layers, = 0.1. The time step length for computation of the flow is 20s while the time step length for computation of the salinity and sediment is 200s. The effect of wind is not considered during the computation of the flow, i.e. = 0. Other parameters for the simulation computations are taken as presented in references [2] and [3].

The data available for the numerical simulation are a tide process of 53 hours from 9:00 hours on December 19, 1991 to 13:00 hours on December 21, 1991, which is in dry season, and a tide process of 53 hours from 17:00 hours on July 15, 1992 to 21:00 hours on July 17, 1992, which is in flood season.

The data of both dry and flood seasons available for the numerical simulation include all the data and information measured and recorded hourly at the 10 water-level observation stations and the 22 observation stations measuring the tidal flow, direction of flow, salinity and sediment concentration, as shown in Figure 1. Data obtained from 6 water-level observation stations and 14 stations measuring the tidal flow, direction of flow, salinity and sediment concentration, which are in the domain of calculation, are simulated and verified. Data obtained from other stations can only be used as the boundary conditions. Results of the verifications show that the computed values of the water-level, vertically-averaged flow velocity, flow direction, vertically-averaged salinity, vertically-averaged sediment concentration, vertical distribution of flow velocity, vertical distribution of salinity and vertical distribution of sediment concentration are all in fair agreement with the measured values[2][3], indicating that the simulation computation has been successful and the 3-D model given in this paper is correct. As the space is limited, the curves of the verifications are not given in the paper.

 

Fig. 1  Topography of the Pearl River estuary and field-measuring stations

3.2  Analyses of results

3.2.1  Characteristics of flow field

Tidal flow is the dominant water flow in the Pearl River estuary, which moves alternately under the joint action of the runoff from the four rivers in the northwest of the estuary and the ebb-and-flow of tides from the open seas (Zhuhai-Lantau Island cross-section and the Hong Kong Waterway) as well as with the influence of the loudspearker-shaped topography and the existence of many islands in the estuary. The prevailing direction of the current is almost north-south. Since the distance from the north to the south of the Pearl River estuary is fairly great, sea water flow has phase difference from the south to the north owing to the influence of the ebb-and-flow of tides from the open seas and the inertia force of the sea water motion itself. It requires two to three hours to get the full flood current from the young flood, or to get the full ebb current from the prime ebb.

The Pearl River estuary is a laminar sea, where the flow velocity is not uniform from the water surface to the bottom and diminishes gradually from the water surface to the bottom. The flow velocity decays slowly with water depth from the water surface to the mid-depth, but the nearer it comes to the seabed from the mid-depth, the faster it decays. The flow velocity at the bottom is 0.4 to 0.7 times the flow velocity at the surface, but the direction of flow from the surface to the bottom is basically the same.

3.2.2  Characteristics of salinity field

The salinity distribution in the Pearl River estuary reflects the mixing process of the runoff water with the shelf water with high salinity from the open seas. The high salinity shelf water from the open seas goes upstream during flooding and its salinity contours move also upstream. The high salinity shelf water which has come up with the flooding water will, together with the runoff water, draw back with the ebbing tide and its salinity contours will also move downstream. During dry seasons, the runoff volume from the four rivers is less and the high salinity shelf water from the open seas covers a long distance to get in, thus the whole Pearl River estuary, except some local areas near the river mouth of Jiaomen, Hongqili, and Hengmen, is basically dominated by the high salinity shelf water and the salinity of the water near Shanbanzhou may be as high as 20‰. However, during flood seasons, the runoff volume from the four rivers is fairly large and, with the resistance and push of the runoff, the high salinity shelf water from the open seas intrudes in for a shorter distance, thus the water area to the north of Neilingdingdao Island in the Pearl River estuary is basically dominated by the sea water diluted by the river water. The salinity of the water near Shanbanzhou is less than 1‰, even the salinity of the waters near Neilingdingdao Island is only between 10‰ and 15‰.The salinity distribution in the Pearl River estuary, whether in dry seasons or in flood seasons, is always high in the south and the east, but low in the north and the west. The salinity contours run northeast to southwest. Such phenomena are the direct result of runoff from Jiaomen, Hongqili and Hengmen. The plane distributions of the salinity field in the Pearl River estuary in dry and flood seasons are given in Figure 2 and Figure 3 respectively.

Fig. 2  Distribution of salinity field in  dry seasons

Fig. 3  Distribution of salinity field in flood seasons

The vertical distribution of salinity in the Pearl River estuary changes with different seasons. In dry seasons, the runoff volume from upstream rivers is rather small and the sea water in the whole Pearl River estuary is very well mixed. As a result, the salinity is basically the same from the water surface to the bottom, even at the observation station set up at Shanbanzhou. However, in flood seasons, as the runoff volume from upstream rivers is fairly large, the salinity in the Pearl River estuary is no longer the same from the water surface to the bottom. Generally, the salinity is low at the water surface but high at the bottom. The salinity at the bottom is about 1 to 3 times that in the surface, indicating that the high salinity shelf water from the open seas covers a longer distance to get in at the bottom than it does at the water surface.

3.2.3  Characteristics of suspended sediment field

Sediment in the Pearl River estuary originates from two sources, one is the sediment transport with river runoff and the other is the secondary transport of sediment on the shoals. It is mainly the latter that is the decisive factor for the distribution of sediment concentration. The distribution of the sediment concentration in the Pearl River estuary is characterized by the following.

(1) The sediment concentration in the shoals is higher than that in the troughs, which is the inevitable result of the secondary transport of sediment in the shoals.

(2) In the Pearl River estuary, high sediment concentration is observed in West Shoal. Although the sediment concentration is also high in Middle Shoal and East Shoal at the time when the external dynamic force is greater, its magnitude is small and duration is shorter, if compared with the sediment concentration in West Shoal.

(3) The peak value of sediment concentration in the Pearl River estuary is mainly resulted from large fall of tide. The peak value of sediment does not synchronize with the peak value of maximum flow velocity, but 2 or 3 hours behind.

(4) The sediment concentration in flood seasons is higher than that in dry seasons and higher in the west than in the east .

(5) There is a sudden transition of sediment concentration (turbid water frontal surface line) between the high sediment area in West Shoal and the navigational channels in the Pearl River estuary. With the rise and fall of the tide, the frontal surface line runs in an irregular zigzag, but the zigzag of the frontal surface line basically remains in West Shoal and, generally, it doesn't enter the navigation channels (Fig. 4 and Fig. 5).

Fig. 4  Distribution of sediment in dry  seasons

Fig. 5  Distribution of sediment in flood seasons

The distribution of sediment concentration, whether in dry season or in flood seasons, is not uniform along the water depth. However, the non-uniform distribution in flood seasons is more clearly remarkable than in dry seasons. Generally, the sediment concentration gradually increases from the surface to the bottom.

4  CONCLUSIONS

The paper presents a 3-D mathematical model of flow-salinity-sediment which is established with the technique of vertical -coordinate transformation together with the finite difference method. In the flow model, the mean flow velocity on the vertical can be used as the open boundary conditions, which can be very conveniently used in practical operations. On the basis of the simulation results, the plane features and the vertical structural features of the flow, salinity and suspended sediment in the Pearl River estuary in both dry and flood seasons are analyzed. The model has no restrictions on the sea areas and can be popularized and widely used. The results of the simulations can be used as a data base and provide boundary data and information for the mathematical models which study and investigate the local sea conditions for any coastal engineering projects in the Pearl River estuary.

References

[1]     Li Mengguo and Cao Zude, 1999. A Review on Tidal Current Numerical Modeling in Coastal and Estuarine Waters, Acta Oceanologica Sinica, 21(1), 111-125. (in Chinese).

[2]     Li Mengguo and Xu Hongming, 1995. Three-Dimensional Mathematical Model of Tidal Flow, Salinity and Sediment in the Pearl River estuary. Technical Report for National Key Scientific & Technological Projects in the Eighth Five-Year Plan Period, Tianjin Research Institute of Water Transport Engineering. (in Chinese).

[3]     Li Mengguo, 1996. Numerical Simulation of the Three-Dimensional Flow Field of Ling Ding Yang, Journal of Hydrodynamics, Ser. A, 11(3), 342-351 (in Chinese).