5) APPLICATION TO THE BAY OF MARMARIS

5.1 CALCULATIONS

By using the graphs in the appendix, the discharge at any given wavelength, wave height, height h and at any two of the slopes tan q may be calculated. This would be useful if a hydraulically or mechanically movable channel is built. By forecasting the weather and the wave conditions in the open seas, the discharge can be estimated. Therefore, the channel may be set up according to the forecasted weather conditions.

From the cumulative wave height non-exceedence probability graphs of the bay of Marmaris , which has been supplied by the Turkish Navy, the following data was obtained:

Marmaris Bay Wave Height Non-Exceedence Probability Data For Each Month (seconds/year)
Wave Height(m)	January	February	March	April	May	June
(0.0,0.5)	9,50E+04	0,00E+00	3,15E+05	5,50E+04	2,50E+05	2,50E+05
(0.5,1.0)	1,89E+05	1,58E+05	4,73E+05	2,48E+05	3,92E+05	5,92E+05
(1.0,2.0)	4,40E+05	8,20E+05	7,57E+05	4,79E+05	7,88E+05	6,70E+05
(2.0,3.0)	2,21E+05	1,58E+05	2,21E+05	2,60E+05	1,05E+05	8,40E+04
(3.0,4.0)	2,21E+05	1,58E+05	9,50E+04	1,05E+05	0,00E+00	0,00E+00
Wave Height(m)	July	August	September	October	November	December
(0.0,0.5)	3,02E+05	2,38E+05	5,50E+05	2,35E+05	0,00E+00	0,00E+00
(0.5,1.0)	4,36E+05	5,88E+05	4,94E+05	4,68E+05	3,86E+05	1,55E+05
(1.0,2.0)	7,20E+05	8,71E+05	9,21E+05	6,73E+05	5,30E+05	8,21E+05
(2.0,3.0)	2,66E+05	3,15E+05	2,67E+05	3,58E+05	3,50E+05	2,09E+05
(3.0,4.0)	0,00E+00	1,23E+05	1,41E+05	1,22E+05	1,53E+05	1,89E+05
Wave Height(m)	Total (sec/year)
(0.0,0.5)	2,29E+06
(0.5,1.0)	4,58E+06
(1.0,2.0)	8,49E+06
(2.0,3.0)	2,81E+06
(3.0,4.0)	1,31E+06

Using the data above, how many seconds per year a range of wave height is present can be calculated. By using the average wave heights of a range, periods of these waves can be evaluated. And by using these values, Ru and the discharge can be calculated. The following are the values of a channel which has a width of 450m, and an h of 0.2m. (see appendix for the equations used)

Wave Height(m)	Average Wave Height(m)	Period (s)	Ru (m)	Q(m 3 /s/m)	Q(m 3 /s)
(0.0,0.5)	0,25	3,00	0,4871	0,4702	211,6082
(0.5,1.0)	0,75	3,50	0,9843	3,0079	1353,5404
(1.0,2.0)	1,50	5,00	1,9886	10,9499	4927,4551
(2.0,3.0)	2,50	6,00	3,0808	23,6704	10651,6899
(3.0,4.0)	3,50	7,50	4,5565	43,3070	19488,1637

As a result, total water flushed into the bay in one year is 1.04 * 10^11 m^3 .

Also, the volume of the Bay of Marmaris had been calculated from a bathymetric map of the bay (i.e. showing the depths of water at different parts of the bay). The volume of the Marmaris Bay came out to be 4.137 * 10^8 m^3 . Therefore, 250 times the volume of the Bay of Marmaris of water will be input each year to the bay by the channel.

5.2 NUMERICAL MODELING

5.2.1) Introduction

After the physical experiments were conducted, it was seen that longitu dinal motion of water could be transformed into a translational flow by means of the wave pump . It is decided to develop a numerical hydrodynamic model of the Marmaris Bay in order to see the effects of the proposed mechanism on the existing circulation in the area. Therefore, a hydrodynamic model study based on the results of the previous set of experiments was carried out and the efficiency of the proposed mechanism was evaluated.

5.2.2) Model Software

A program named “MIKE21” was used to model the Marmaris Bay hydrodynamics. MIKE21 is a professional engineering software package containing a comprehensive modelling system for 2D free-surface flows. It is developed by the Danish Hydraulic Institute. Detailed information about the program can be found here.

5.2.3) Model Setup

a) Model Area

Model area covers whole Marmaris Bay including two straits at the entrance. The maximum water depth in the area exceeds 50m. The open boundary of the model area is located outside the bay.

For the hydrodynamic model setup of the Marmaris Bay , the bathymetry has been input firstly. A two and three dimensional view of the model bathymetry are given in fig3 and fig4 . Total model area is around 8.5 km x 7.5 km.

Fig 3

Fig 4

b) Grid Spacing

For the bathymetry, the grid spacing was decided to be ?x = ?y = 25m. Grid spacing was chosen to be 25m-25m to ensure the enough resolution of the bathymetry, i.e. the false neck (the thinnest part of the land) could be easily drawn with this resolution. The model area is defined by a 340 x 320 grid points.

c) Time step, ? t

Time step was chosen to be 5 seconds, which corresponds to a Courant Number around 5.

d) Initial & Boundary Conditions

Initial conditions: The initial surface elevation at the start of the simulation is chosen to be 0, assuming a totally calm condition at the start. Therefore, first few time steps of the model results during the warming up period were discarded in the result evaluations.

Boundary conditions: From the model open boundary, a tidal time series of 40 cm amplitude and 12 hours period was input.

e) Other Model Parameters

Bed resistance is the resistance of the seabed to the incoming waves or current and essentially used for model calibration. In the tests the bed resistance was set to the constant value of 32 (m/s) ^1/3 in terms of Manning Number.

Eddy viscosity is another calibration parameter which controls the size of the horizontal eddies in the area. Due to lack of field data a constant value of eddy viscosity of 0 is assumed.

Wind :In the model tests no wind condition was assumed.

5.2.4 Advection Dispersion (AD) Modeling

The AD module of Mike 21 simulates the spreading of dissolved substances subject to advection and dispersion process.

For the AD models, a polluting substance, which completely dissolves in water, is used. Initially, the inside of the Bay of Marmaris is assumed to be polluted 100% and the outside assumed to be not polluted at all. Then, by inputting water at a discharge rate that had already been calculated depending on the physical experiments, from the points selected along with the tide, results are obtained.

•  AD model no 1 (tide only)

To estimate the effect of tide on the pollution inside the bay, an AD model without any input of water other than tide was made. For this model, a semi-diurnal tide with a height of 40 cm was used. A semi-diurnal tide of a height 40 cm was used, because according to the previous works of Arti Proje Ltd. Co. and some other universities in the area, this was the average tide setting for the Bay of Marmaris .

•  AD model no 2 (source 1 and tide)

For this model, water with a discharge rate of 5113 m^3/s was input from source 1(see fig5 ) and a semi-diurnal tide with a height of 40 cm was defined.

Fig 5

•  AD model no 3 (source 2 and tide)

For this model, water with a discharge rate of 5113 m^3/s was input from source 2 (see fig5 ) and a semi-diurnal tide with a height of 40 cm was defined.

•  AD model no 4 (source 1 and 2 and tide)

For this model, water with a discharge rate of 5113 m^3 /s was input from both source 1 and source 2 (see fig5 ) and a semi-diurnal tide with a height of 40 cm was defined.

Results:

After each of the experiment was done, an animation in .flc format and a series of pictures in .jpeg format were produced. For these animations and pictures, please go to the animations section.

To compare the results obtained from the modelings, one-dimensional models at selected points on the model were made. From the results obtained from these modelings, graphs of percentage pollution versus time were drawn. These graphs are below:

Percentage Concentration at P (200,50) versus Time

 

Percentage Concentration at P (290,150) versus Time

 

Percentage Concentration at P (220,160) versus Time

 

Percentage Concentration at P (150,220) versus Time

5.2.5) Hydro Dynamic (HD) Modeling

The HD module of Mike 21 simulates the water level variations and flows in response to a variety of forcing functions in lakes, estuaries and coastal areas.

For the HD models, the same setup in section 5.2.3 was used. The same models as in the AD modeling were made with the same discharge rates same tide settings and by using the same point sources.

5.3) CONCLUSION

As can be inferred from the graphs in section 5.2.4, tide by itself doesn't have much effect on the pollution inside the bay. However, if the wave pump were built on the selected places, the pollution would be cleaned in a short period of time.

However, the discharge rate that we used in these AD and HD models is unnecessarily high, because this discharge cleans most of the bay in less than three days. Since the bay is not polluted up to 100% in three days by the external factors, the discharge rate can be reduced by narrowing the channel width to a value that is much less than 100 m. By reducing the discharge rate, the current inside the bay would be reduced too, which would enable the vehicles in the water move easier and reduce the effects of the wave pump on the living organisms inside the bay.