Salient Calculation at the Single Offshore Breakwater for a Wave Perpendicular to Coastline using Polynomial Approach

Coastal protection planning using offshore breakwater requires an estimation on the formed salient. There are research results using physical model as well as field observation on the relation between the length of breakwater and the position of breakwater with the formed salient. The relation, however, is qualitative in nature. This research develops a calculation method for a formed salient in single offshore breakwater as a result of a wave that is perpendicular to the breakwater. The model is developed based on the characteristic of stable coastline, i.e. stable coastline that is parallel to the wave crestline forming it, whereas the salient equation is approached with polynomial. The equation provides a good result, i.e. the measurement of salient that is very much in accordance with the result of previous research using physical model or field measurement. Keywords— Offshore Breakwater, Coastal protection planning, Polynomial Approach, surf zone area.


INTRODUCTION
Many coastal protection using offshore breakwater or detached breakwater have been constructed. The construction is in the form of breakwater that is parallel to the coastline, within the surf zone area with a quite close distance with the coastline. At the coastline protected by offshore breakwater, sedimentation will occur where the sediment deposit is called salient (Fig.1). The efficiency of breakwater is measured from its salient condition. Although it is called offshore breakwater, the real location is quite close with the coastline in order to produce salient or tombolo, where the incoming wave is almost perpendicular or even perpendicular to the coastline. Therefore, this research formulated salient equation for the incoming wave perpendicular to breakwater and the coastline. An important factor in offshore breakwater planning is the formation of salient, where the success of this coastal protection is in the formation of the salient. The dimension (small and large) of a salient is expressed by the distance of the top of salient with the original coastline, i.e. (Fig.1.)

Fig.1. Offshore breakwater and salient
Quite a few researchers have conducted research on the measurement of salient , but it is only qualitative in nature. Those researchers are among others: Ahren and Cox (1990), Leo C. Van Rijn (2013), Inman and Proudcy (1966), Nir (1982) and many more whose research results will be discussed in Chapter III. The result of the research is presented in the form of a comparison between the length of breakwater with the breakwater distance to original coastline ( ) with salient type, but it is only qualitative and is not expressed as a relation between with the salient height . . It is stated that the bigger the value of the higher of salient height will be where in a

Fig. 2. Stable coasline with its forming crestline.
This research is developed based on the static equilibrium condition, where the tangent of the stable coastline is similar with the tangent of its forming crestline ( Fig.2) with the goals of obtaining practical method in conducting salient measurement, i.e. the peak ordinate of salient . Salient equation is approached with polynomial of degree 10 so there are 11 polynomial coefficients that must be determined. The calculation of polynomial coefficient is done using the characteristic of stable coastline as has been mentioned.

II. STUDY ON THE CHARACTERISTIC OF STABLE COASTLINE
This section will show that stable coastline condition is parallel with crestline, using longshore sediment transport equation and an example of geometry stable coastline exists in the nature.

2.1.
Review of longshore sediment transport equation formula. Coastline changes are mainly caused by longshore sediment transport, where evolution coastline model, such as GENESIS uses longshore sediment transport equation as the basic equation. The longshore sediment transport equation is a function of the angle between crestline of the breaking wave against coastline, where if the crestline is parallel to the coastline, it will produce zero longshore sediment transport or no erosion and sedimentation or the coastline is in stable condition.

a.
Kamphuis' Longshore sediment transport formula, Kamphuis longshore sediment transport rate, = subscript denoting breaking condition; a complete information can be seen at Kamphuis, J.W. (1991). The concern of this equation is the element 0.6 ( 2 ) , where =angleof breaking waves to local shoreline. In this case, if = 0, the tangent of crestline is parallel or equal to the tangentof the coastline, then = 0.
Similar to equation (1), the concern is the element In the case of Ƌ Ƌ = 0or is very small, then equation (3) becomes, In this equation (4) = 0, then = 0. Complete information on equation (3), can be seen atHanson, H., and Kraus, N.C. (1989). From the three longshore sediment transport equations, it can be stated that at the stable coastline, the tangent of the coastline is parallel or equal to the tangent of the crestlinethat forms the coastline. In an open area where the coast is formed by incoming wave, the tangent of the coastline is parallel with the crestline of the incoming wave, whereas at the shadow zone, stable coastline is parallel with the crestline diffracted wave.

Review on the form of stable coastline.
It has been known that in the nature there is geometrical form of the stable coastline in static equilibrium condition, and there are plenty of researches that have been done on  From the review of the longshore sediment transport equation and the geometry of stable coastline, it can be concluded that stable coastline has a tangent that is parallel with the crestline forming it. For the coastline directly facing the incoming wave, the tangent stable coastline is equal to the tangent of the crestline of the incoming wave, whereas the coastline formed by the diffracted wave will have a tangent that is equal to the tangent of diffracted wave crestline. This condition will be used as boundary condition at the formulation of stable coastline equation.

III. SOME RESULTS OF PREVIOUS STUDIES
There are plenty of previous researches in the formulation of salient at the offshore backwater. This section will present some results of previous studies that will be used in the model development. The results of the research are in the form of qualitative relation with the salient and do not mention about wave angle.

3.1.
Ahrens and Cox (1990) Ahrens and Cox (1990) used the beach response index classification scheme of Pope and Dean (1986) to develop a predictive relationship for beach response based on ratio of the breakwater segment length to breakwater distance from original shoreline. The relationship defining a beach respose index is : ....... (6) where the horizontal axis is coincided with the original coastline (Fig.4). The number of polynomial terms is an effort to obtain a unique solution, where the more the number of polynomial terms, the more will be the boundary conditions that are used so that they will increase the solution uniqueness . There are two boundary conditions, i.e. the two ends of the salient, where in this section an assumption is done that coastline coordinate is fixed. Whereas at the interior points, the boundary condition of the stable coastline is done, i.e. coastline tangent or salient which is similar to the tangent of the wave forming it. The wave forming salient is diffracted wave, whereas the direction of diffracted wave is defined as in Fig. 4. Thus, the salient characteristic formed by diffracted is symmetrical. In this method there is an assumption that in the salient growth, the tangent of a point is still the same, from the beginning of the formation until the final condition. To obtain the values of polynomial coefficients 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 and 10 , boundary conditions are done at the points as presented in Table 3. The abscissa values of the boundary tangent condition points is the result of an experimentation to obtain a salient condition that in accordance with the Vanrijn and Ahren&Cox criteria. At the salient equation and its boundary condition there is no wave height impact or diffraction coefficient since crestline tangent is not determined by wave height or diffraction coefficient. Whereas salient tangent is determined by crestline tangent.      On the other hand, Table 5 presents the result of the calculation with changing breakwater length ,whereas the breakwater distance is fixed at 30 m, which also provides a result that is in accordance with the result of the research by Ahren and Van Rijn. Thus, it can be concluded that the model that is developed provides a very good result. The comparison between the result of the calculation in Table 4 with the result of the calculation in Table 5 shows that at the same value of , different value was obtained , i.e. is bigger at bigger , as an example for = 1.5, in Table 4., ( = 60 , = 40 ), = 9.28 , meanwhile in Table 5. ( = 45 , = 30 ), = 6.95 . VI. CONCLUSION There is a conformity between the result of the model with the result of the previous research which is the result of field observation as well as the result of physical model in the laboratory. Thus it can be concluded that the method that was developed is capable of modeling the formation of salient and tombolo well. However, the obstacles in this method is the determination of interior abscissa of the boundary condition points was done like an experiment, where with different interior abscissa of the boundary condition points will result in different result. Therefore, further development needed is formulating equation for determining the boundary condition interior points or looking for additional equilibrium equation so that the result of the model is no longer dependent on the location of the interior boundary condition points.