A Numerical Modeling for Study Marine Current in the Manado Bay, North Sulawesi

This study is investigating about marine currents provided electrical energy through the numerical model. The objective of this study is to know the power available distributions in the Manado Bay, North Sulawesi, Indonesia. The Manado Bay was width 2200 m with 79 m of depth. In computation, we are made grids in x and y horizontal were 7 m respectively, also for z vertical of four layers. The results shown that the power available distributions in the Manado Bay at 0.1 Sv were 0.00-20.00 kW/m 2 when low tide currents and when high tide currents were 0.00-105 kW/m 2 . The values will enable for marine currents power plant in the Manado Bay to future.

where u (x,y,z,t), v (x,y,z,t), and w (x,y,,z,t) are the velocities in horizontal directions of x, y, and z-direction respectively, η(x,y,t) is the elevation of free surface, t is the time, eff ν is an effective diffusion taking of account turbulent viscosity and dispersion, , cor f is the Coriolis parameter, assumed to be constant, and g is the gravity.

Turbulence Model
The equation of turbulence that used was turbulent viscosity from the mixing-length model [15,16] as follow: where l h and l v are horizontal and vertical mixing length scales respectively.

Boundary Conditions
In the numerical study here, the boundary conditions need to be set as [14]: by the bottom, by the surface of the water [17], by boundaries which can be vertical impermeable structures (wall), and by boundaries in the open sea [18]. The power available in the Manado Bay, we can be obtaining from Equation [19][20]: where P in kW/m2, v is

Numerical Model
The numerical method that used was semi-implicit finite difference for the 3D in Equation (1), (2), and (3) was used by: [1], [3], [12], [15], and [21][22][23]. Figure 1 shows choices adopt in the vertical direction. The velocities are defined on the edge of the mesh, we guessed virtual meshes to write the limiting conditions with the walls, and we decorate the free surface with the grid.
The generally, we can be written semi-implicit discretization in Equation (1) and (2) in the compact matrix form [1] as follow: Then, the velocity vertical in Equation (3) If we are discretization Equation (5), then the power available becomes: where P is the availability power in the Manado Bay (kW/m 2 ) and respectively.  Figure 2 shows flow chart for solution of a numerical model in calculating the velocities of u , v and w respectively and the power available in the Manado Bay. The "calculate components of the velocities (u, v and w) and power available" symbol are show a process for calculating of horizontal velocities u in Equation 6 and v in Equation 7 with a linear threediagonal, whereas for calculating velocity vertical w use Equation (8). Finally, calculating the power available where the calculation used Equation (9). The "n" symbol shows the quantity of calculating with iteration do-process until maximum iteration (T max ). The "T > T max " symbol is the process to execute determination when the iteration has been greater than maximum iteration, if no then process will be go to "n" for continue to calculate again, and if yes then it go to "finish".

Method
The position of Manado Bay in Indonesia and numerical area are located in the Sulawesi Sea with approximately 300 km 2 of the area as shown in Figure 3 and width of about 2.2 km between Bunaken Island and Sulawesi Island, and down to 79 m deep.
We are made two types of simulations in 3D-simulations with one discharge. There are four layers to deep. In calculation, there are 174 x 318 mesh in x, y directions with Δx = Δy = 7 m. Also, we are used four vertical layers and the integration time Δt = 0.4 sec as shown in Table 1, and discharge is 0.1 Sv (1 Sv = 10 6 m 3 /s). Figure 4 illustrates the bathymetry 3-D and 2D of the Manado Bay which used for numerical simulation.
Tide predictions were computed based on the Admiralty method using Harmonic Constants taken from the Indonesia Sailing Direction and the results of the Hydro-Oceanographic surveys. Information about tide is needed for the safety of navigation as mention in navigational Indonesia regulation number 21, 1992 [24]. Hourly heights of tide of 95 stations

Results and Discussion
We can see that the power available distributions when high tide currents (Figure 6b Whereas at enter channel in Singkil river of 0.5-8 kW/m2. It is caused due to the confluence of the river and the marine currents, also, the flow of river water to move freely into the sea with an average depth of 2 m. The distributions of the power available when low and high tide currents in the Manado Bay (3D-simulation) at discharge 0.1 Sv respectively showed in Figure 7. Tide currents very influence to the power available which very big at high tide current [25][26][27]. When low tide currents, the distributions were 0.00-20.00 kW/m 2 and 0.00-105.00 kW/m 2 when high tide currents in the Manado Bay.

Conclusion
Study on marine current in the Manado Bay, North Sulawesi, Indonesia through a numerical model has been successfully accomplished. The maximum of power available at discharge of 0.1 Sv when low and high tide currents were 20 and 105 kW/m 2 respectively. The results will be enabling to design the turbines that used in the marine current power plant in Manado Bay in the future.