1. Yellow River Institute of Hydraulic Research, YRCC, Zhengzhou 450003, China

2. Department of Civil Engineering, Tianjin University, Tianjin 300072, China

Abstract:This paper applies the one-linemodel to Yellow River estuary shoreline change, which has complicated flow with hyper-concentration sediment. The paper consists of two parts;the first describes the principles of the shoreline model,and the choice ofthe model'sparameters.As an important factor,a breaking wave model,in which the combined deformation of wave refraction,diffraction and shoaling is considered. Especially, the river sediment distributing contributed for shoreline changes is considered. The second part presents the results of numerical simulation of shoreline change on Yellow River estuary .The results ofnumerical simulation agree with the shoreline change situation observed well.

Key words:shoreline change, prediction, wave breaking, one-line model, Yellow River estuary

1. Introduction

The erosing recede of sandy shoreline is the popular problem in the world. Recent decades, the Yellow Rivercoastal regions become an importantplace for economical, ca1turd,recreational,tourism actions. Therefore, the erosing recede ofshoreline causes severely disastrous loss. Therefore, the research and prediction of Yellow River estuary shorelinechange is a very important subject.

The research of shoreline change is concerned in a long-term shoreline evolution, and with large limit,from several thousand meters to several kilometers. And the physical mechanism is very complex, hence it is not efficient to investigate this problem by physical model (i.e., hydraulic mobile bed model).In fact, the numerical model for studying the coastal dynamic configurationis a more ideal means at present, there is not the scale effect in numerical model,it is very easy to change parameters of model, the cost is very cheap, the time is saved, the results can be of fairly high precision while various factors are considered reasonably.

The shoreline model is based on the method of Peinard-Consider in 1956, assuming the beach profile does not change in the process of shoreline evolution. It is suitable to simulate change of longer shore (several thousand meters to several kilometers) during longer term (several months to several years).The wave conditions, structures and sediment transport affect the shoreline change by considering their average values. The application is rather mature in the engineering practice. Excepting one-line model, other models need a definite description for the cross-shore sediment transport, but the investigation about the cross-shore sediment transport is very poor. That restricts the application of those models. Hence the one-line model is the most suitable and actual at present and is accepted by engineers. Up to now, in the model the one of the basic equations-the long shore sediment transport rate equation is being perfected, providing the fundamental for calculating shoreline evolution accurately; the calculation method of wave deformation is developing for more accurate and more practical approach.

2. Main theory of shoreline model

A basic assumption in the one-line model is that the active beach profile moves in parallel to itself within a certain closure depth, beyond which the long shore sediment transport can be ignored and the profile does not change. According to the sediment continuous equation, the rate of change in onshore and offshore element volume connects with the change of shoreline, and then shoreline position is given by equation

                                                (1)

where x and y are alongshore coordinate and cross-shore coordinate respectively, x-axis points to  offshore, y-axis parallels to the regional trend of the shoreline ;t is the time (s);Q_l is the volume rate of long shore sediment transport (m³/s);  is the volume rate of sediment entering and leaving, D_C is the closure water depth the profile from landward and seaward boundaries which is defined as vertical distance from top of beach to the seaward limit of the zone of active the high region effected by the change of beach profile (Fig.1).

Fig. 1  Sketch for sediment balance

In the situation without the berm, D =D_C Kraus (1983) suggested applying Hallermeier limit depth of significant sediment transport (using incident wave condition) as the closure depth:

                                   (2)

Where  and  are deep water wave height and wavelength.

Equation (1) shows that the difference between the net rate of sand entering and leaving the section equals the rate of the deposition or erosion; the time rate of the shoreline change and the alongshore change of sediment transport rate is adapted to each other; and the long shore sediment .This is the transport rate and wave condition are adapted to each other at every point of shore. This is the essence of one-line model.

3. Breaking wave induced long shore sediment transport rate

Breaking wave induced long shore sediment transport rate is applied:

                              (3)

Where  is wave height;  is wave group velocity from linear wave theory; subscript b denotes the dimensionless parameters and  is defined as follows:

where and  which are adjustable are empirical coefficients and are determined in calibration ;  is the porosity of sediment;  is the average beach slope ; is angle between the breaking wave crest and shoreline.

The breaking wave characteristics,  andare given by the breaking wave model. In practice, the wave model plays an important role. The solution of shoreline equation is determined by the initial condition, the boundary conditions and the parameters of the mode1.Because the initial condition is immediate, the boundaries are standard, in essence, the solution of the shoreline equation is determined by the parameters of the model. And the parameters relate to the breaking wave height and angle close. Fundament of practical breaking wave model is the most important part of one-line model.

First, calculating the wave direction angle, the following equation is given

                                                   (4)

Where  is wave number;is wave direction angle.

Let  and, substituting A and B into EQ (4) gives

Then, the wave direction angle is

                                                              (5)

In the stable wave field, the conservation equation of the wave energy flux can be expressed as

                                                  (6)

And wave height can be induced from EQ (6) as follows:

                                                              (7)

Based on Snell theory, breaking wave direction angle as follows:

                                                            (8)

Where C_b and  are the wave celerity and wave angle while waves break.

4. River sediment transport rate on Yellow River estuary

Besides long shore sediment transport, river estuary outlet sediment is an important component for shoreline changes. About 1.6 billions t sediment outlet to Bohai Sea every year. In Eq. (1)  denote the river sediment distributing applied for shoreline changes. In this paper, use Li Zegang et al. analysis the sediment distributing characteristics for river hydraulics.

5. Verification for model

The shoreline change during 365a from September 1987 to September 1988 is verified. Fig. 2 is the field measured fathom line in 1987 and 1988. Using the parameters in calibration model and adopting the wave data of 1988 year. The result is shown in Fig.3. The result of verification not only agrees with change value from sea chart, but also with the analysis result from another method.

Fig.2. Field measured fathom line in 1987 and 1988     Fig.3. Compare for calculating shoreline with 

measured shoreline

6. Conclusion

(1)The one-line model for shoreline change on Yellow River estuary is setup and the result of verification (from 1987 to 1988) not only agrees with change value from sea chart but also with the material analysis result.      

(2)The principle of coastal dynamics and one-line model are employed to determine the parameters in the numerical model, especially for Yellow River complicate flow with hyper concentrated sediment.

(3)The model could be used for Yellow River estuary shorelines changes prediction after more verification.

References

Qin Chongren and He JiangCheng, Acta OceanologicaSinica,Vol16, No.3, pp403-407, 1997

Li Z G.Basic hydrologicfeatures nearthe Yellow River estuary area [J].Journal of Oceanography of Huanghai & Bohai Seas, 2000, 18(3):20-28.

Goda Y., T. TakaYama and Y.Suzuki, Diffraction diagrams for directional random waves. Proceedings of 16th costal Engineering conference, ASCE, pp.628-650.

Hallermeier R.J. Uses for a calculated limit depth to beach erosion, Proceedings of 16th costal Engineering conference, ASCE, pp.1493-1512.

Kraus N.c. Application of a shoreline prediction model. Proceedings of costal Structures, 83, ASCE, pp.632-645.

Source:  www.yellowriver.gov.cn   Editor:HuangFeng