Salient Modeling at offshore Breakwater for oblique wave using least Square weighted Residual Method

— This research is the continuation of previous research by the writerusing polynomial approach with the purpose of fixing various constraints in the previous method. The salient equation used in this research is similar to the one used in the previous research, i.e. the principle of static equilibrium coastline where the tangent of the stable coastline is similar to the tangent of the crestline. In the previous method, the salient equation was approached with a polynomial equation, then polynomial coefficient is obtained by applying the first differential (tangent) of the polynomial in various points with the number of points that is in accordance with the number of polynomial coefficient. There is an obstacle in this method, i.e. the setting of boundary condition points that should be done with trial and error In this research the tangent equation of the salient is approached with polynomial equation using five points of sample. Salient equation is also approached with polynomial. To obtain polynomial coefficient, the first differential of the salient equation is equalized with tangent equation of the salient and Least Square Weighted Residual Method is applied. Unlike previous research, there is no constraint in this research using this method. Comparison with the result of the research from previous researches shows a conformity of the result of the model with the result of the previous research.


INTRODUCTION
Offshore breakwater is a breakwater constructed parallel with the coast. Even though it is called offshore breakwater, the position of the construction is quite close with the coast, where the construction efficiency is very much determined by the distance between the breakwater and the original coastline. On the coast protected by offshore breakwater, sediment deposit will be formed which is called salient. The success of coastal protection using offshore breakwater is determined by salient that was formed (Fig.1), where the height of the salient is determined by the length of breakwater and the distance between breakwater and the original coastline or breakwater distance . Considering that breakwater is constructed quite close with the coast where the crestline is almost parallel with the coast or the wave direction is almost perpendicular to the coast (Fig.2), thereforein this research a breakwater is developed for a wave that is perpendicular to the coast.

Fig.1. Offshore breakwater and salient
This research is working on an assumption that longshore sediment transport is the primary cause of the changes in coastline.Longshore sediment transport equation of some researcher, such asKomar, P.D., (1998), Shore Protection Manual (SPM), (1984), Van Rijn, Leo C. (2013), Mill-Homens, J.,Ranasinghe, R., Van Thiel de Vries, J.SM. and Stive , M.J.F., (2013), is the sine function of the breaker crest line angel where the value of Longshore sediment transport is zero or no longshore sediment transport if the breaker crestline is parallel to or forming zero angle against the coastline. In other words, in a stable coastline, the tangent of breaker crestline is similar to the tangent of the coastline (Fig.2).This condition becomes the basis of salient equation in this research.

Fig. 2. Crestline ofoblique waves
This research aims at obtaining the method of salient height (Fig.1) for a breaker length , at a breakwater distance X. This research is the continuation of a previous research by the writer where in the previous research polynomial approach was applied where the value of the polynomial coefficient is obtained by applying stable coastline equation on various points (boundary point) on the original coastline. In the previous research, the difficulty was found in determining boundary points. In this research, salient equation is also approached with polynomial, where polynomial coefficient is obtained by using Least Square Weighted Residual Method with Galerkin procedure (Stassa, F.L. (1985)), whereas the tangent of salient is approached with a polynomial equation using five sample points. Some previous researchers have made relation between ( , )with salient height but in qualitative form i.e. relation ( , )with the type of salient that was formed. Those researchers areAhrens, J.P, ad Cox, J.

II. SOME LONGSHORE SEDIMENT
TRANSPORT EQUATIONS As has been mentioned in the previous section that longshore sediment transport equations from some researchers are the sine function of breaker crest line. The next section will show some longshore sediment transport equations.
Ɵ with a value of zero if crest line is parallel to or similar to the coastline. Therefore, the tangent of salient will be similar to the tangent of the diffracted crestline.

III. SOME RESULTS OF THE PREVIOUS STUDIES
There have been many researches on salient formation at offshore breakwater. This section will present some results of previous researches that will be used as comparator on the model development. The results are in the form of qualitative relation between and salient without mentioning wave angel.

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 ( Table 1).
The relationship defining a beach respose index is :  Nir (1982) and SPM (1984) also conform with both criteria. Tangent Crestline Equation on Breakwater Lee. Salient model in this research is developed with an assumption that salient is formed by diffracted wave, therefore it requires tangent from diffracted wave that can reach the coastline.In the calculation of this crestline angle, an assumption was applied that the tangent crestline on a point with abscissa on original coastline is fixed, even though ordinate changes due to the changes in bathymetry in the process of salient formation. The second assumption on the calculation of this crestline angle is that crestline angle is symmetrical, with its center

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Vol-7, Issue-2, Feb-2020]  https://dx.doi.org/10.22161/ijaers.72.32  ISSN: 2349-6495(P) | 2456-1908(O) www is the number of polynomial term where the degree of polynomial is − 1 and in this research = 5 was used. The calculation of polynomial constant was applied with least square method using 5 (five) interpolation points as on Table 3 and Fig.3., with the definition of crestline angle in Fig.4.. As an example, the result of the interpolation of the tangent value crestline angle for = 50 m, with = 25 m and = 50 m is presented in Fig (3). Fig.3 shows that the value of = ( ( ))at = 25 m is bigger than at = 50 m which shows that the salient curve for = 25 m is bigger than the salient curve at = 50 m. This also shows that the closer the position of breakwater to the coastline, the higher the salient height will be.    (Table 2). Table 5 presents the result of the calculation for changing length of breakwater, whereas breakwater distance = 50 m.Similar result is obtained namely at = 3.5 permanent salient is formed. However, there is a difference between the result on Table   4 and on Table 5. As an example, on = 50 m and = 33.33, = 6.25 m is obtained, whereas on Table 5., at = 1.5, where = 75 m and = 50, = 9.375 m is obtained. This result shows that in the salient formation, breakwater length plays more role than breakwater distance.