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Wave modifications in a semi-cnclosed basin: bahia concepcion

University of Florida Institutional Repository

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1 WAVE MODIFICATIONS IN A SEMIE NCLOSED BASIN: BAHIA CONCEPCION By HANDE CALISKAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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2 Copyright 2006 by Hande Caliskan

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3 ACKNOWLEDGMENTS I would like to thank to my a dvisor Arnoldo ValleLevinson fo r his substantial help, moral support and patience throughout this study, my comm ittee members Robert G. Dean and Andrew B. Kennedy for assisting me with their valuable knowledge, and Alexandru Sheremet for helping me to find the suitable model for my study. I also would like to thank to my wonderful pare nts, for their endless love and trust in me and finally my friends for their incredible support. Nothing would be as good as it is right now without you

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........5 LIST OF FIGURES................................................................................................................ .........6 ABSTRACT....................................................................................................................... ..............8 CHAPTER 1 INTRODUCTION................................................................................................................... .9 2 METHODS........................................................................................................................ .....11 3 RESULTS AND DISCUSSION.............................................................................................22 Observational Results.......................................................................................................... ...22 SWAN Wave Model Results..................................................................................................24 4 CONCLUSIONS....................................................................................................................66 LIST OF REFERENCES............................................................................................................. ..67 BIOGRAPHICAL SKETCH.........................................................................................................68

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5 LIST OF TABLES Table page 2-1 CPU and wall-Clock times fo r three different grid sizes...................................................21 2-2 Test cases................................................................................................................ ...........21 3-1 Coordinates of the points wher e the frequency spectra is obtained...................................32 3-2 Coordinates of significant wave height observation points...............................................33 3-3 Percent reduction in significant wave height.....................................................................33 3-4 Differences in Hs and energy dissipation for the ca ses without bottom friction (Case 1); without bottom friction and depth indu ced wave breaking (C ase 2); and without bottom dissipation, depth induced wave breaking and whitecapping (Case 3).................33 3-5 Percent reduction in en ergy per unit wave ray length due to combined effects of bottom friction, depth-induced breaking and whitecapping; refraction and diffraction....33

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6 LIST OF FIGURES Figure page 2-1 Bahia Concepcion and Measurement Stations...................................................................17 2-2 Comparison of Contour Plots of Signi ficant Wave Height for Available Friction Models in SWAN Wave Model.........................................................................................18 2-3 Comparison of Contour Plots of Ener gy Dissipation for Available Friction Models in SWAN Wave Model......................................................................................................19 2-4 Contours of Significant Wave Height for Different Grid Sizes.........................................20 3-1 Wave Energy Contours and Wind Velocity Vectors at ST1 between November 2004 and February 2005.............................................................................................................34 3-2 Wave Energy Contours and Wind Veloci ty Vectors at ST1 between February 2005 and April 2005................................................................................................................. ..35 3-3 Wave Energy Contours and Wind Veloci ty Vectors at ST1 between April 2005 and June 2005...................................................................................................................... .....36 3-4 Wave Energy Contours and Wind Veloci ty Vectors at ST1 between June 2005 and August 2005.................................................................................................................... ...37 3-5 Wave Energy Contours and Wind Veloci ty Vectors at ST1 between August 2005 and November 2005..................................................................................................................38 3-6 Wave Energy Contours and Wind Veloci ty Vectors at ST2 between November 2004 and February 2005.............................................................................................................39 3-7 Wave Energy Contours and Wind Veloci ty Vectors at ST2 between February 2005 and April 2005................................................................................................................. ..40 3-8 Wave Energy Contours and Wind Velocity Vectors at ST2 between April 2005 and June 2005...................................................................................................................... .....41 3-9 Wave Energy Contours and Wind Veloci ty Vectors at ST2 between June 2005 and August 2005.................................................................................................................... ...42 3-10 Wave Energy Contours and Wind Velocity Vectors at ST2 between August 2005 and November 2005..................................................................................................................43 3-11 Graphical Representation of the Poin ts where 1D Wave Spectra was Requested.............44 3-12 Spatial Energy Density Contours in J/m2 for BC1, BC2 and BC3....................................45 3-13 Spatial Energy Density Contours in J/m2 for BC4, BC5 and BC6....................................46

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7 3-14 Spatial Energy Density Contours in J/m2 for BC7, BC8 and BC9....................................47 3-15 Significant Wave Height Contours for BC1, BC2 and BC3..............................................48 3-16 Significant Wave Height Contours for BC4, BC5 and BC6..............................................49 3-17 Significant Wave Height Contours for BC7, BC8 and BC9..............................................50 3-18 Mean Wave Direction Contours for BC1, BC2 and BC3..................................................51 3-19 Mean Wave Direction Contours for BC4, BC5 and BC6..................................................52 3-20 Mean Wave Direction Contours for BC6, BC7 and BC8..................................................53 3-21 Average Absolute Period Contours for BC1, BC2 and BC3.............................................54 3-22 Average Absolute Period Contours for BC4, BC5 and BC6.............................................55 3-23 Average Absolute Period Contours for BC7, BC8 and BC9.............................................56 3-24 Energy Dissipation Contours for BC1, BC2 and BC3.......................................................57 3-25 Energy Dissipation Contours for BC4, BC5 and BC6.......................................................58 3-26 Energy Dissipation Contours for BC7, BC8 and BC9.......................................................59 3-27 Spatial Energy Density Contours in J/m2 for BC2 and the Case without Bottom Friction, Depth-Induced Breaking and Whitecapping.......................................................60 3-28 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 2 and 25 m...61 3-29 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 50 and 100 m.............................................................................................................................. ..........62 3-30 Spatial Energy Density Contours for BC2 and BC2 without Diffraction..........................63 3-31 Spatial Energy Density Contours for a Fl at Bottomed Rectangular Bay with a Depth of 100 m....................................................................................................................... ......64 3-32 Distance from the Mouth vs. Energy Density Plots for Cases BC2; BC2 without Diffraction.................................................................................................................... ......65

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8 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science WAVE MODIFICATIONS IN A SEMI-E NCLOSED BASIN: BAHIA CONCEPCION By Hande Caliskan December 2006 Chair: Arnoldo Valle-Levinson Major: Coastal and Oceanographic Engineering In order to determine wave climatology in Bahia Concepcion, year long records of bottom pressure were obtained at the mouth and head of the bay. Wind waves were predominantly produced by southeastward winds in the winter and northnorthwestward winds in the summer. Only 3, 7 and 15 second waves were recorded at the mouth of the bay, i.e. wave energy was produced only by 3, 7 and 15 second waves there. At the head of the bay 3 second waves dominated the wave energy. The energetic long-per iod swell waves were dissipated in the bay as they were not observed at the head of the bay. This study sought to identify the effects that caused the swell waves to attenuate in the bay. Numerical model results showed that long-period swell waves were attenuated b ecause of the combined effects of bottom friction, refraction, diffraction and wave blocking. Most of the atte nuation, however, was caused by wave blocking owing to the change of orientation of the bay.

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9 CHAPTER 1 INTRODUCTION Wave Climatology in semi-enclosed basins has been studied numerous times at different sites all around the world. One of the common find ings in these studies has been the observation that ocean swell vanishes at some distances into the bay. For exampl e, Boon et al., (1996) observed that in Chesapeake Bay ocean swell waves were attenuated before they reach the middle of the bay. Similarly, according to L ong and Oltman-Shays (1991) observation ocean swell waves attenuated at th e open coast of Duck, NC. According to their study in 1991, two dimensional wave spectra were used at two different point s, one of which was closer to the coast. One of the observations was that wave fre quency was higher and direction was nearly perpendicular to the bottom contours at the poin t closest to the coast. At the offshore point, frequency was lower and waves were propagati ng with a greater approach angle. This observation has been used to hypothesize that the cause of the attenuation of ocean swell waves was refraction. To my knowledge, this hypothesis has been the only attempt to explain the reason for the attenuation of swell waves. This study is motivated by the observation that low frequency waves (~ 7 s) were dissipated in Bahia Concepcion, in the Gulf of Californi a (Figure 2-1). In-situ data recorded at two different stations suggested th e influence of waves with periods of 5 7 s at the entrance but waves with periods less than 5 s at the head. However, the main purpose of the data collection was determining along-bay pressure gradients. Da ta were recorded according to the requirements of the main purpose that might not have had appropr iate temporal coverage to yield a reliable set of data for wave climatology studies. In order to test the concept of wa ve attenuation in Bahia Concepcion a numerical wave model, SWAN, was used first to be able to validate the reliability

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10 of the data, secondly to find the possible reasons behind the attenuation a nd finally to show the contribution of various dissi pating effects on attenuation. The study area is located on the Gulf of California side of the Baja California peninsula between the longitudes of -111o 58 8 and -111o 40 6 and the latitudes of 26o 32 21 and 26o 54 57 (Figure 2-1). Bahia Concepcion is exposed to st rong winds from NW with a speed more than 10 m/s for extended periods along it s axis during the wint er and spring seasons (BadanDangon et al., 1991). Its bathymetry is qu ite simple. Immediately after the bay entrance, there is a deep and narrow channel with an av erage depth of 30 m at the east side of the bay mouth. The deepest point of the ba y is located on this channel and the depth there is 34.5 m. The bay entrance, with a width of 5.95 km, is located 39.98 km away from its south end point and the bay width varies between 3.40 and 10.38 km. The west side of the bay, close to the mouth, has the mildest bed slope causing an extended shallow zone from the coast. In this shallow zone, between the latitudes of 26o 42 31 and 26 o 45 13 there are several islands. The names of the islands are Isla San Ramon, Isla Pitahaya, Isla Blanca, Isla Bargo, Isla Guapa and Tecomate. Semi-diurnal tidal height is observed to be 150 cm at the entrance and 36 cm at the head of Gulf of California. The minimum semi-diurnal tidal height in the Gulf of California is observed in its central regions with a value of 5 cm because of the existence of an semi-diurnal amphidromic point. (Marinone et al ., 2003). Since Concepcion bay is located at th e Central Gulf of California, tidal forcing along the bay is weak.

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11 CHAPTER 2 METHODS In order to determine alongbay pressure grad ient, bottom pressure was recorded every 15 min at the mouth and head of the bay (Figure 2-1). These measurements were obtained between November 2004 and October 2005. Data were record ed with SBE26 instruments deployed at a depth of 5.10 m at the mouth and 5.70 m at the h ead of the bay, below the mean sea level and these stations are labeled as ST1 and ST2, respectiv ely (Figure 2-1). In the mean time, wave data were recorded with a frequency of 4 Hz at 30 s bursts every 3 hrs. One of the most important inputs for determin ing the surface wave field is the wind data because of its high contribution to wave deve lopment and growth. For this study, wind data (wind velocity) were recorded using Aanderaa an emometers with a frequency of 1 Hz. For this purpose instruments were installed 10 m above the mean sea level at the mouth and the head, at distances less than 1 km from the bottom pressure recording stations, ST1 and ST2. Although it was possible to measure wind waves w ith the available instruments, there was no apriori intention of resolving the wave fiel d. Once again, the main purpose of the deployment was to observe the pressure gradient s along the bay. But in order to assess whether the wind wave patterns observed were reliable, Concepcion Bay was modeled using the Simulating Waves Nearshore Model (SWAN Model). The latest version available for public use, SWAN Cycle version 40.41, was used for this study. Wave prediction models have been improved according to the impr ovements on the wave evolution knowledge. First generati on models did not consider nonl inear wave interactions while second generation models included these interactions through some parameterizations. On the other hand, third generation wave models used an explicit source te rm for non-linear wave interactions (Hasselmann et al., 1985). SWAN is a third generation, numer ical wave prediction

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12 model that uses the known bathymetry, wind and current conditions for wave parameter estimations. The model uses the wave action balance equation, which can be expressed in Cartesian coordinates as (Hasselmann et al., 1973) T y xS N c N c y N c x N c t N '' where N ( , ) (= E( )/ ) is the action density, E( ) is the wave energy density, is the intrinsic frequency (i.e., frequency of wave components according to a reference moving with the local current), t is time, ST is the source term, is the wave direction and cx, cy, c , c are the propagation velocities in x, y, and spaces, respectively. Each term of this equation can be explained as follows: t N = Local rate of change of action density, x N cx = Propagation of ac tion in x direction, y N cy = Propagation of ac tion in y direction, '' N c = Shifting of relative frequency due to depth and current variations, N c = Refraction due to depth and current variations, TS = Source term for wave energy growth due to wind, wave energy transfer due to nonlinear wavewave interactions and wave energy diss ipation due to bottom friction, depth induced breaking and whitecapping. For this study, inputs to the model were ba thymetry, wind velocity and wave forcing. A southeastward wind of speed 10 m/s is used for th e base case of the st udy because the bay is

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13 exposed to southeastward winds with speeds exc eeding 10 m/s for extended periods. In addition, waves were prescribed from the N bounda ry with an approach angle of 30o, a wave height of 1.5 m and a wave period of 10 s. The reason for pr escribing waves with these parameters is to represent the ocean swell waves entering the bay to be able to observe the changes that will occur as they propagate towards the head. Th e outputs requested from the model were one dimensional (frequency) spectra, significant wave height, mean wave direction, energy dissipation, average absolute wave period and mean absolute wave period. For all tests, nonlinear quadruplet wave interactions, depth induced wave breaking, wh itecapping, bottom friction and wind generation were activated to be able to obtain closer results to real life conditions. SWAN has three optional formulations for friction calculations, which are: The empirical JONSWAP model (Hasselmann et al., 1973), Eddy viscosity model of Madsen et al. (1988), Drag law model of Collins (1972). Using the available data it is not possible to ma ke a calibration for bottom friction. Therefore, in order to decide what friction formulation to use, a test was conducted. Th ree different cases were run with the same boundary c onditions, same southward wind of speed 10m/s. The only parameter changed for these cases was the frictio n model. Although friction factors within each formulation can be modified as required, default values were used for this test. Figures 2-2 and 2-3 show contour plots of signi ficant wave height and energy di ssipation over the bay for the three friction models. According to the results obtained from this test, there was not much difference in the general patterns of the contour plots. However, it was clear that the model of Collins gave lower estimates of friction than both JONSWAP and Madsens model. When the models of Collins and Madsen were compared, it was seen that the greatest difference in energy dissipation was 0.1843 W/m2 at the mouth of the bay and was in the range of 0.18 0.49 W/m2

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14 along the breaker zone where most of the waves break. There is a ~20 m shoal at the mouth of the bay between the longitudes of -111o 52 56 and -111 o 52 12 and latitudes of 26o 51 23 and 26 o 52 41 (Figure 2-1). The depth decreases by 6 m at the bar and it is very likely that waves feel the bottom and dissipate on it. The m odel of Collins gave low estimates for energy dissipation over this bar and th erefore JONSWAP and Madsen fo rmulations were considered further. When JONSWAP and Madsens models were co mpared it was seen that Madsens model gave greater energy dissipation values. The larg est difference between the model estimates was at the mouth, on the shoal, with a value of 0.17 W/m2. Even though the dissipation estimates were slightly different from each other, this only affected the significan t wave height by 1.8cm. Since this difference was very small when compar ed to the wave height it can be said that Madsens formulation produced consistent resu lts with JONSWAP for this specific case. According to the test results and knowing the fact that SWAN uses JONSWAP model as its default setting, JONSWAP was chosen to be used in this study. Default values for the coefficient of the JONSWAP form ulation are: 0.038 m2/s3 for swell conditions and 0.067 m2/s3 for wind sea conditions. In this study, both swell and local wind waves exist but SWAN does not have a default value to consider both swell and wind sea conditions and with the available data it was not possible to make a calibration for the JONS WAP formulation coefficient. Therefore, both coefficients for swell and wind sea conditions we re tested and it was obs erved that when the coefficient for swell conditions was used dissipa tion values were too sma ll to be realistic and therefore, 0.067 m2/s3 was used for the rest of the study. Secondly, a sensitivity test for the m odel spatial resolution was conducted. The computational grid that was used to generate re sults was determined using this sensitivity test.

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15 For this test, three different grid sizes were se lected for the same wind speed and direction to observe the sensitivity of the calculations to the resolution. A southeastward wind with a speed of 10 m/s (the predominant wind di rection for the bay in winter), was selected to drive the model with grid sizes of 100, 200 and 400 m both in the x a nd y axes. When compared to the finest grid (100m), the 400m grid size was unable to resolve the details properly especially along the shore due to inaccurate values obtained by interpol ating a point inside the bay where the wave parameters can be calculated and a point outsi de the bay where wave parameters cannot be calculated. On the other hand, the grid size of 200 m was able to resolve the bay better than 400m showing enough details for the purpose of this study. Figure 2-4 shows a comparison of these th ree grids for significant wave height calculations. As the grid size increases, the mode l tends to overestimate the significant wave height. The percent difference of significant wave heights between the grid sizes of 100m and 200m was less than 1% whereas between 100m a nd 400m, the difference increased to 4% along the mid-span of the bay. Moreover, increasing the grid size made the mode l unable to resolve the details along the shoreline. For example, usi ng a grid size of 400m cau sed the islands, between the longitudes of -111o 54 8 and -111 o 51 43 and the latitudes of 26o 42 31 and 26 o 45 13 to disappear. On the other hand, a grid size of 200m was not only able to show enough details for the purpose of the study, but also it saved a c onsiderable amount of CPU and wall-clock time (Table 2-1). The grid size of 200 m was chosen for the rest of th e studies because it achieved the required resolution and it saved a cons iderable amount of time for each run. After determining the grid size, different cas es for different wind speeds and directions were run. The main purpose of these tests was to compare the behavior of waves at ST1 and ST2, where observations were available;

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16 to compare different model results w ith the available observational data; to observe the behavior of waves under different wind speed conditions; and to observe the differences due to different wind directions u nder a constant wind velocity. First of all, the sensitivity of the wave parameters, such as significant wave height, wave period and mean wave direction, to wind speed variability was te sted with a fixed azimuth of 150o and wind speeds of 5, 10 and 15 m/s. It should be noted that, here and throughout this study, wind and wave directions will be presented according to oceanographic convention. In other words, the direction where the wind is blowing (or the wave is propagating), is measured clockwise from the North. Secondly, wind speed was kept constant at 10 m/s and variability of the wave parameters as a result of the wind di rection change was observed. All test cases are summarized in Table 2-2.

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17 Figure 2-1 Bahia Concepcion and Measurement Stations ST2 ST1 Shoal

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18 Figure 2-2 Comparison of Contour Plots of Significant Wave Height for Availabl e Friction Models in SWAN Wave Model

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19 Figure 2-3 Comparison of Contour Plots of Energy Dissipation for Available Fr iction Models in SWAN Wave Model

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20 Figure 2-4 Contours of Significant Wave Height for Different Grid Sizes

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21 Table 2-1 CPU and wall-Clock times for three different grid sizes Grid Size (m) 100 200 400 Total CPU Time 7029.81 1725.39 394.98 Total Wall-Clock Time (s) 46240.12 1871.61 413.74 Table 2-2 Test cases Name of the Case Wind Speed (m/s) Wind Direction (o) BC1 5 150 BC2 10 150 BC3 15 150 BC4 10 180 BC5 10 120 BC6 10 50 BC7 10 20 BC8 10 90 BC9 10 0

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22 CHAPTER 3 RESULTS AND DISCUSSION This chapter contains two sections. In the firs t section of this chapte r, results derived from the data collected by the bottom mounted instru ments will be presented. The second section includes the detailed model results and a compar ison of them with the observational results. Observational Results As mentioned before, wind velocity data were recorded at ST1 and ST2 with a frequency of 1 Hz. To be able to eliminate high frequenc ies in the wind data, Lanczos filter, which is a lowpass digital filter, was used. Then wind veloci ty vectors are decimated and plotted for every 3 hrs over the full deployment dur ation at the mouth (Figures 3-1b 3-5b) and at the head (Figures 3-6b 3-10b). In these plots, directi on of the vectors demonstrates where the wind is blowing to and magnitude of the vectors demonstr ates its speed. The scale for the speed is shown on the y-axis in m/s. It should also be noted that there were missing data due to recording problems, especially at the mouth of the bay. Th ese periods are marked with a horizontal dashed line plotted at zero velocity to di fferentiate the recording durations. Figures 3-1a 3-10a show contours of wave energy, plotted in time and frequency space. As a matter of fact, in these plot s, each section cut vertically would represent the wave spectrum of a burst that was recorded at the time of th e selected section. The reason for plotting these wavelets was to give a better representation of the observed wave energy with different frequencies over the full depl oyment duration. Energy (in cm2) here is defined to be the sum of the variances over each frequency band. For exampl e, contours plotted for a wave period of 7 s show the sum of the variances for the frequencies between 1/8 and 1/6 Hz. Figures 3-1a 3-10a and 3-1b 3-10b are pr esented for the same periods of time and plotted one on another to be able to show the high correlation between wind velocity and wave

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23 action. As the data suggest, when wind speed increases, wave action usually increases too. However, for the cases of strong eastward or west ward winds, it is not po ssible to observe this correlation. The main reason for this weak corre lation is the short fetc h in the east west direction. The data suggest that wave action in th e bay is highly correlated with the speed of winds blowing along the axis of the bay (winds fr om NW NE) because of its longer fetch that allows waves to grow. Contour plots at the mouth of the bay (Figur es 3-1a 3-5a) show that wave energy is mostly concentrated on 3 s waves and it is pos sible to observe some energy on 13 s waves. However, in reality more energy could be concen trated on low frequency waves (i.e. periods of 13 s or more). It is not possibl e to observe this with the avai lable data because each burst consisted of a 30 s recording interval. Such an interval may not be enough to capture enough number of low frequency waves to be able to show the actual energy they have. On the other hand, the data set for the head of the bay shows that wave energy has decreased considerably although wind speed has not decreased more than 20%. For instance, 1315 s waves have completely disappeared, it is not possible to observe as much energy on 5 s waves as at the mouth and even the energy on 3 s waves that can be produced by local winds has decreased considerably. (F igures 3-1b 3-5b) The reduced wave activity at the head of the ba y is either caused by tr ansfer or by loss of wave energy and the reasons for that might be refraction, shoaling, bottom friction, whitecapping or any combination thereof. To see if the computational model will give similar results to what has been observed and to be able to understand the r easons of low frequenc y wave attenuation at the head, the SWAN wave model has been r un and results obtained are presented in the following section.

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24 SWAN Wave Model Results Figures 3-12, 3-13 and 3-14 show the spect ral energy density distributions in J/m2/Hz derived from the SPEC1D comman d of SWAN model, which gives the onedimensional spectra, for all of the test cases presented in Table 22. These contours were pl otted for the frequency range 0.05.5 Hz using the spectra that were obtained at 20 different points selected approximately in the middle of the bay from mouth to head. Coordinates of the selected points are presented in Table 3-1 and locations are show n in Figure 3-11 with a st ar. The ordinate axis of the contour plots show the distances from th e head in meters meaning that the zero point shows the mouth of the bay. All contours, regardless of wind speed and direction, show that the bay has a behavior of attenuating the highly energetic l ong waves as they propagate toward the head. It is possible to see that approximately around 15 km from the mo uth most of the low frequency waves were dissipated in all cases. On the other hand, highe r frequency waves exist everywhere along the bay. This behavior was also one suggested by th e field data. Therefore, model results suggest that observational data presented in the previous section have a reveali ng pattern of the wave behavior in the bay. As mentioned previously, BC1, BC2 and BC3 cases were run to see the response of the bay to wind speed change under the same wind direction and wave fo rcing conditions. Energy density contours of these cases are presented in Figure 3-12. One of the major differences in these three plots is the frequency range of waves at the head of the bay. It is seen that the frequency range at the head of the bay increases as the wind speed increases. For BC1, wind speed is 5 m/s and the frequency of most of the waves reaching the head ranges between 0.28 and 0.50 Hz, giving a range interval of 0.22 Hz. For BC2 where the wind speed is 10 m/s this range is between 0.18 and 0.50 Hz causing the inte rval to increase to 0.32 Hz. The frequency

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25 range for BC3 (wind speed = 15 m/s) is betwee n 0.14 and 0.50 Hz and the range interval is 0.36 Hz. This suggests that stronger winds can genera te waves with a wider range of frequencies when compared to weaker winds. The response of the bay to th e wind direction change is di splayed by the energy density contours for BC2 and the cases BC4 BC7 (Figur es 3-12, 3-13, 3-14). When the bay is under the effect of southward southeastward winds, (Figures 3-12 and 3-13 for BC2, BC4 and BC5) energy contours were very similar to each other. In other words, even adverse winds did not affect the distance traveled by the swell waves. The only difference observed was at the locally generated short wind waves. When the wind was blowing from between we st and south; the di stance, along which the low frequency waves attenuated, was equal to the distance for cases BC2, BC4 and BC5. However, the frequency of the waves that reached the head of the bay decreased considerably. This is due to the effect of the adverse wind a nd the direction the prescr ibed waves at the mouth of the bay. Since the wind was blowing from th e opposite direction, waves were dissipated as they propagated towards the head. This caused th e frequency of the waves that were able to reach to the head to further decrease. (Mitsuyasu, 1997) As stated previously, at tenuation of low frequency waves was observed from the in-situ data and the SWAN model was used to verify th e reliability of the observational results. Since the model results verified that the observationa l results were reliable, the SWAN model results were also used to determine the reasons for a ttenuation of the low frequency waves as they propagated towards the head. As mentioned be fore, significant wave height, mean wave direction, average wave period a nd energy dissipation ou tputs were requested from the model.

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26 These parameters are presented in contour maps and used both for reinfo rcing the observational results and finding a reasonable ex planation to what has been observed (Figures 3-15 3-26). Significant wave height (Hs) contour maps show that for all cases, Hs decreases considerably from the mouth to a distance of 6 km into the bay (Figures 3-15 3-17). This attenuation mainly occurs on the west side of the bay entrance. The 30 m deep channel on the east side of the mouth does not have a significant effect on Hs attenuation. Furt her into the bay, Hs increases slightly for the case of southwar d and southeastward winds (for cases BC2, BC3 and BC5) because the wind causes waves to grow along the longest fetch in the bay. Although the wind direction for BC1 (wind speed = 5 m/s) is the same as BC2, BC3 and BC5, there is a decrease in Hs. This indicates that when the wind is not strong enough, its growing effects on waves is not enough to overcome the attenuati ng effects such as refr action, diffraction and bottom friction. When the wind is blowing from other directions than between N and NW, Hs continues to decrease as the waves propagate towards the head. For cases BC7 and BC9 even after passing the narrow channel close to the mouth of the bay, Hs attenuation continues at a higher rate than other cases. This is caused by the dissipation effect of the opposite directions of the wind and wave propagation. To s ee the percent reduction in the Hs three different points are selected, one at the mouth of the bay, one after th e dissipative channel and one at the head of the bay. Table 3-2 and Table 3-3 show the coordinates of these points and the percent reduction in the significant wave height relative to the point at the mouth, respectively. For BC1, BC2 and BC3 significant wave he ight maps show an increase in Hs pattern all over the bay as the wind speed increases from BC1 to BC3 (Figure 3-15). This indicates the well known wave behavior that the wind speed has a direct effect on wave generation and wave growth (Jeffreys, 1924). When the contour maps fo r the rest of the cases are observed, the first

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27 difference one can notice is the lo cations of the areas where the Hs is less than 0.2 m (Figures 316 and 3-17). These calm areas exist if the wi nd direction is not aligned with the swell propagation direction and their lo cations depend mainly on the magnitude of the y component of the wind. If the y compone nt dominates the wind as in cases BC7 and BC9, a low energy area is located at the SW whereas if the east co mponent starts to dominate, this area elongates towards the NW into the islands. Figures 3-18, 3-19 and 3-20 show mean wave dire ction contours that re veal the patterns of refraction. By looking at these contour maps it can be said that this final version of SWAN can predict refraction quite well even around the islands to the south of the latitude 26o 42 36 Since it has been observed that the SWAN wave model is capable of calculating the refraction, the contribution of the refraction to the low frequency wave attenu ation will be presented in the following sections of this chapter. Dense contours at the mouth of the bay and along the channel in average absolute wave period contour maps (Figures 3-21, 3-22, 3-23) cl early show the attenuation of low frequency waves. At the deep channel on th e east side (immediately south of the bay entrance) the wave period change is not as large as it is on the west side. This may s uggest that the swell attenuation is related to the depth and this will be investigated in the foll owing sections of this chapter. Energy dissipation (W/m2) contour maps illustrate the su m of various processes: depth induced wave breaking, bottom friction and whit ecapping (Figures 3-24, 3-25, 3-26). From these plots, it is clearly seen that a relevant cause of significant wave hei ght attenuation and average mean period maps is energy dissipation. It is possible to see the hi gh correspondence of energy dissipation with Hs and average mean period especially at the locations where strong attenuation occurs. For example, at the bay entrance, where water depth decreases by 6 m, it is possible to

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28 observe higher rates of energy di ssipation and significant wave he ight. It should also be noted that the reduction in the dept h here may also have a contri bution to the swell attenuation. After determination of the corresponden ce between energy dissipation and significant wave height attenuation, three mo re cases were run to observe th e effect of bottom friction, wave induced breaking and whitecapping to the signifi cant wave height and the wave spectra. New cases were generated by changing the dissipation formulations of the base case, BC2, without changing the bathymetry, wave and wind conditi ons. In the first case bottom friction was reduced by introducing a very small coefficien t into the JONSWAP formulation ([cfjon] = 0.0001 m2/s3) to be able to see the co ntribution of bottom friction to the low frequency wave attenuation. For the second case the coefficient of JONSWAP formulation was kept at 0.0001 m2/s3 and in the mean time, the depthinduced wave breaking option of SWAN was turned off. Finally, for the third case whitecapping was turned off in addition to the conditions in case 2. These three cases were compared with the ba se case, BC2, and the maximum differences of significant wave height and ener gy dissipation between the new cas es and BC2 are displayed in Table 3-4. These results showed that the greatest difference occurred at the shallow section of the bay entrance (especially over the sand bar). The most significant contribution to energy dissipation was from bottom fric tion with a value of 16.636 W/m2 and this caused the highest attenuation in Hs with a value of 3.02 m. According to th e results presented in Table 3-4 depth induced wave breaking and whitecapping do not have a significant effect on the energy dissipation. As a matter of fact it is possible to see the great est effects of depthinduced breaking at the breaking zone. However, for the purpose of this study data at the breaking zone was not examined. Although it was possible to observe the differences in en ergy dissipation and Hs due to bottom friction, depthinduced wave break ing and whitecapping sepa rately, Figure 3-27

PAGE 29

29 shows that these factors do not affect the wave sp ectra significantly. It on ly shows the spectra for the base case, BC2, and the case without bo ttom friction, depthinduced wave breaking and whitecapping. Even in this case, the spectra for th ese cases are almost identical and this suggests that attenuation (or ener gy dissipation) of the waves as they propagate towards the head is not greatly affected by bottom friction, de pthinduced breaking or whitecapping. The previous test showed that the attenuati on of the low frequency waves was not affected significantly by the components of energy dissipation. Additional reasons for the low frequency waves to attenuate can be the refraction and shoaling. Since both refraction and shoaling are depthdependent occurrences, some changes were made on the bathymetry file to observe the change in the behavior of the low frequency waves. For this pur pose, three new cases were run with a wind velocity and wave forcing the same as the base case, BC2, but with flat bathymetries of depths 2, 25, 50 and 100 m. It should be noted that the JONSWAP fricti on coefficient, depth induced breaking and whitecapping options were not changed or turned off for the new cases. Depths were chosen to be able to observe the be havior of the bay in shallow, intermediate and deep water conditions. Waves can be categorized as shallow water waves, intermediate depth waves and deep water waves according to the fo llowing conditions (Dean and Dalrymple, 1991): 10 kh Shallow Water Waves kh 10 Intermediate Depth Waves kh Deep Water Waves where k is the wave number and h is the water depth.

PAGE 30

30 Using these conditions, a wave period of 10 s (w ave period selected for model calculations) and the dispersion relationship, kh gk tanh2 where g is the gravitati onal acceleration, one can obtain the depths separating shallow water from in termediate depth and intermediate depth from deep water. These depths were found to be 2. 38 and 77.87 m, respectively. Figures 3-28 and 329 show the one dimensional wave spectra for th ese cases. The plot for 2 m represents shallow water waves, plots for 25 and 50 m represent intermediate depth and 100 m represents deep water conditions. From these figures it is possi ble to observe that lo w frequency waves can propagate further into the bay as the water depth increases (i.e. as the waves propagate in deeper water). For instance, for shallow water (depth of 2 m), 10 s waves canno t be observed after 500 m into the bay from the mouth, but for intermediate depths of 25 and 50 m, it is possible to observe them up to 20 km. On the other hand on e may expect to observe low frequency waves further into the bay for the deep water case. Howe ver, model results showed that even for a depth of 100 m low frequency waves disappeared 22 km before reaching the head. Because bathymetric effects were eliminated by introduci ng a flat bottom, and hence refraction effects were suppressed, one possible reason for the wave dissipation was the geometry of the bay. The bay did not have a straight geom etry causing waves to be blocked as they propagate, especially at latitudes 26o 42 36 and 26o 46 48 At locations where the pr opagation of low frequency waves was blocked, energy was distributed late rally, perpendicular to the dominant wave direction and thus waves attenuated. This phe nomenon is called wave diffraction (Dean and Dalrymple, 1991). The version of SWAN that was us ed for this study has th e ability to consider the effects of diffraction and in this particul ar case, since the bathymetric effects were eliminated, it may be possible to observe diffrac tion effects. However, since diffraction is more effective in small-scale models, one other case wa s added to verify the ef fects of diffraction. In

PAGE 31

31 this case diffraction was eliminated from the ba se case, BC2, and wave spectra are presented in Figure 3-30. As the figures suggest diffraction affects swell waves at the mouth of the bay where dimensions are relatively smaller than the rest of the bay. However, its effect decreases as the waves propagate into the bay and hence it is not possible to observe sw ell waves beyond 16 km. Since it is not possible to observe swell waves at the head of the bay even after eliminating bottom friction, refraction and diffraction, one final case is added to be able to observe the effect of bay geometry. In this case, th e bay geometry was replaced by a rectangle with a width of 7 km and a length of 42 km. Once agai n a flat bottom in deep water conditions (100 m) was selected and waves were prescribed to propagate southw ard from the north boundary of the bay with a wave height of 1.5 m and wave period of 10 s. Wave propagation directio n was changed for this case to be able to make the propagation direct ion perpendicular to the bottom contours. In addition to these, bottom friction was reduced once again by assigning the coefficient of JONSWAP to be 0.0001 m2/s3. Figure 3-31 shows the wave spectra for this case and as it can be observed from the figure, some low frequency wave s were able to propagate from the mouth to the head without attenuation. Figure 3-32 shows the distribution of the wa ve spectra along the distance from the bay mouth to the head, at a wave frequency of 0.1 Hz for the cases BC2; BC2 without bottom friction, depthinduced breaking and whitecapping; fl at bottom with a water depth of 100 m; and rectangular bay without bottom friction, dept hinduced breaking and whitecapping. With the original bay geometry, even for the most ba sic case where bottom friction, depth-induced breaking, whitecapping, refraction and diffractio n were eliminated, energy density curve decreases from mouth to the head. However, when bay is replaced with a rectangle with the same dimensions, wave energy kept constant. This show s that most of the swell waves could not reach

PAGE 32

32 the head of the bay because of the blocking effect of the land. In additi on, it has been observed that diffraction, bottom friction, whitecapping and depth-induced break ing have very small contribution to swell attenuation. Refraction has the most contri bution to the swell attenuation, especially close to the bay mouth where wa ves had not been blocked by the land. The contributions of refraction, diffraction and the combined effect of bottom friction, whitecapping and depth-induced breaking were calculated from the areas unde r the energy density curves and are represented in Table 3-5. This table shows mo st of the contribution to the swell attenuation is caused by refraction close to the mouth and the effect of diffraction, bottom friction, depth induced breaking and whitecappi ng is negligibly small. Table 3-1 Coordinates of the points wh ere the frequency spectra is obtained X Coordinate (m) Y Coordinate (m) 7769.3599 41578.6016 8584.3398 39341.1992 9562.3301 36637.6992 10540.2998 33561.1992 11681.2998 31417.0000 12278.9004 29366.0000 12604.9004 27315.0000 12713.5996 25543.6992 13039.5996 22747.0000 13256.9004 20416.3008 14180.5996 18458.5000 14886.9004 16966.9004 15484.5996 15195.5996 16625.5000 13610.7998 17657.9004 12305.5996 18472.8008 10441.0996 19831.0996 8483.3398 21352.5000 6432.3701 22765.0996 4101.7100 24014.6992 1491.3800

PAGE 33

33 Table 3-2 Coordinates of significan t wave height observation points Point at the Mouth Point after the channel Point at the head Longitude -111.8781 -111.8398 -111.7208 Latitude 26.8835 26.7807 26.5608 Table 3-3 Percent reduction in significant wave height % REDUCTION IN SIGNIFICANT WAVE HEIGHT Test Cases Point after the channel Point at the head BC1 70.53 72.80 BC2 43.62 39.32 BC3 31.88 20.76 BC4 47.71 47.95 BC5 53.64 45.71 BC6 57.97 60.01 BC7 52.59 91.49 BC8 52.60 58.23 BC9 48.33 94.64 Table 3-4 Differences in Hs and energy dissipation for the cases without bottom friction (Case 1); without bottom friction and depth induced wave breaki ng (Case 2); and without bottom dissipation, depth induced wave breaking and whitecapping (Case 3). Difference Between Max. Difference in Energy Dissipation (W/m2) Max. Difference in Hs (m) Case 1 and BC2 16.621 3.020 Case 2 and BC2 16.636 3.051 Case 3 and BC2 16.639 3.069 Table 3-5 Percent reduction in en ergy per unit wave ray length due to combined effects of bottom friction, depth-induced breaking a nd whitecapping; refraction and diffraction. Attenuation due to % Reduction in Energy Refraction 14 Combined effect of bottom friction, depth-induced break ing and whitecapping < 1 Diffraction < 1 Blocking of land 84

PAGE 34

34 Figure 3-1 Wave Energy Contours and Wind Velocity Vect ors at ST1 between November 2004 and February 2005

PAGE 35

35 Figure 3-2 Wave Energy Contours and Wind Velocity V ectors at ST1 between February 2005 and April 2005

PAGE 36

36 Figure 3-3 Wave Energy Contours and Wind Velocity Vectors at ST1 between April 2005 and June 2005

PAGE 37

37 Figure 3-4 Wave Energy Contours and Wind Velocity Vectors at ST1 between June 2005 and August 2005

PAGE 38

38 Figure 3-5 Wave Energy Contours and Wind Velocity Vectors at ST1 between August 2005 and November 2005

PAGE 39

39 Figure 3-6 Wave Energy Contours and Wind Velocity V ectors at ST2 between November 2004 and February 2005

PAGE 40

40 Figure 3-7 Wave Energy Contours and Wind Velocity V ectors at ST2 between February 2005 and April 2005

PAGE 41

41 Figure 3-8 Wave Energy Contours and Wind Velocity Vectors at ST2 between April 2005 and June 2005

PAGE 42

42 Figure 3-9 Wave Energy Contours and Wind Velocity Vectors at ST2 between June 2005 and August 2005

PAGE 43

43 Figure 3-10 Wave Energy Contours and Wind Velocity Vectors at ST2 between August 2005 and November 2005

PAGE 44

44 Figure 3-11 Graphical Representa tion of the Points where 1D Wave Spectra was Requested

PAGE 45

45 Figure 3-12 Spatial Energy Density Contours in J/m2 for BC1, BC2 and BC3

PAGE 46

46 Figure 3-13 Spatial Energy Density Contours in J/m2 for BC4, BC5 and BC6

PAGE 47

47 Figure 3-14 Spatial Energy Density Contours in J/m2 for BC7, BC8 and BC9

PAGE 48

48 Figure 3-15 Significant Wave Height Contours for BC1, BC2 and BC3

PAGE 49

49 Figure 3-16 Significant Wave Height Contours for BC4, BC5 and BC6

PAGE 50

50 Figure 3-17 Significant Wave Height Contours for BC7, BC8 and BC9

PAGE 51

51 Figure 3-18 Mean Wave Directi on Contours for BC1, BC2 and BC3

PAGE 52

52 Figure 3-19 Mean Wave Directi on Contours for BC4, BC5 and BC6

PAGE 53

53 Figure 3-20 Mean Wave Directi on Contours for BC6, BC7 and BC8

PAGE 54

54 Figure 3-21 Average Absolute Peri od Contours for BC1, BC2 and BC3

PAGE 55

55 Figure 3-22 Average Absolute Peri od Contours for BC4, BC5 and BC6

PAGE 56

56 Figure 3-23 Average Absolute Peri od Contours for BC7, BC8 and BC9

PAGE 57

57 Figure 3-24 Energy Dissipation Contours for BC1, BC2 and BC3

PAGE 58

58 Figure 3-25 Energy Dissipation Contours for BC4, BC5 and BC6

PAGE 59

59 Figure 3-26 Energy Dissipation Contours for BC7, BC8 and BC9

PAGE 60

60 Figure 3-27 Spatial Energy Density Contours in J/m2 for BC2 and the Case without Bottom Friction, Depth-Induced Breaking and Whitecapping

PAGE 61

61 Figure 3-28 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 2 and 25 m

PAGE 62

62 Figure 3-29 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 50 and 100 m

PAGE 63

63 Figure 3-30 Spatial Energy Density Contour s for BC2 and BC2 without Diffraction

PAGE 64

64 Figure 3-31 Spatial Energy Density C ontours for a Flat Bottomed Recta ngular Bay with a Depth of 100 m

PAGE 65

65 Figure 3-32 Distance from the Mouth vs. Ener gy Density Plots for Cases BC2; BC2 wit hout Diffraction, BC2 without Diffraction, Bottom Friction, Depth-Induced Breaking and Whitecapping; Flat Bottom for Deep Water Conditions (Depth=100m) and Rectangular Bay without Diffrac tion, Bottom Friction, Depth-I nduced Breaking and Whitecapping

PAGE 66

66 CHAPTER 4 CONCLUSIONS It has been observed both from the in-situ data and model results that the ocean swell waves were attenuated as they propagate into the bay and before reaching the head they completely disappeared. Moreover it was possibl e to observe locally generated high frequency wind waves all around the bay once again from bo th the observational and model results. Even though the data were not collected to study surf ace waves, results gathered from the model studies verified that the observational data ha ve a revealing pattern of the surface waves. The reasons behind the attenuation of the swell waves have found to be: Combined effect of bottom friction, depth-induced breaki ng and whitecapping, Diffraction, Refraction and, Wave blocking. After observing the differences between the refrac tion eliminated case and the rectangular bay case, it has been seen that the geometry of th e bay was reason for swell waves not to reach bay mouth. Waves were blocked by the land especially beyond 20 km into the bay. According to the calculations based on energy, 84% of the swell waves were bloc ked by the land before reaching the head. The contribution of refraction was 14%. Bottom friction, depth induced wave breaking and whitecapping did not seem to have a significant effect on swell attenuation. The combined contribution of them was found to be around 1% to the attenuation. Diffractions contribution was also found to be less than 1%.

PAGE 67

67 LIST OF REFERENCES Badan-Dangon, A., Dorman, C. D., Merrifield M.A. and Winant, C.D. (1991). The lower atmosphere over the Gulf of California, Journal of Geophysical Research 96, C9, pp. 16877-16896 Boon, J.D., Green, M.O., Suh, K.D. (1996). Bimoda l wave spectra in lower Chesapeake Bay, sea bed energetics and sediment tr ansport during winter storms, Continental Shelf Research 16, pp. 1965-1988 Collins, J.I. (1972). Prediction of shallow water spectra, Journal of Geophysical Research 77, 15, pp. 2693-2707 Dean, R. G., and Dalrymple, R. A. (1991). Wate r Wave Mechanics for Engineers and Scientists. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Hasselman, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselman, D. E., Kruseman, P., Meerburg, A., Mller, P., Olbers, D. J. Richter, K., Sell, W. and Walden, H. (1973) Measurements of wind wave growth and swell decay during the Joint Nort h Sea Wave Project (JONSWAP), Deutschen Hydrograhischen Zeitschrift 12, A8 Hasselmann, K., Allender, J. H., Barnett, T. P. (1985). Computations a nd parameterizations of the nonlinear energy transf er in a gravity wave spectrum. Pa rt II: Parameterizations of the nonlinear energy transfer for a pplication in wave models, Journal of Physical Oceanography 15, pp. 1378-1391 Jeffreys, J. (1924). On the formation of the waves by wind, Proceedings of the Royal Society of London A, pp. 107-189 Long, C.E., Oltman-Shay, J.M. ( 1991): Directional characteristics of waves in shallow water, Technical Report CERC-91-1, U.S. Army Engineer Waterways Experiment Station Madsen, O. S., Poon, Y. K. and Graber, H. C. (1988). Spectral wave attenuation by bottom friction:Theory, Proc. 21st Int. Conf. Coastal Engineering ASCE, pp. 492-504 Marione, S.G., Lavin, M.F. (2003) Residual flow and mixing in th e large islands region of the Gulf of California, Nonlinear Processes in Ge ophysical Fluid Dynamics Kluwer Academic, Dordrecht, The Nederlands, pp. 213-236 Mitsuyasu, H. (1997). On the contributi on of swell to sea surface phenomena, International Journal of Offshore and Polar Engineering 4, V7, pp. 241-245

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68 BIOGRAPHICAL SKETCH The author was born in A nkara, Turkey on January 16th 1984. She lived in her hometown Ankara for most of her life. She completed he r primary, middle and high school education at Buyuk High School, Ankara between September 1990 and June 2001. Then she was accepted to the Civil Engineering program of Middle East Te chnical University, Ankara, in September 2001. During her undergraduate education she developed a special interest in Coastal Engineering after taking several courses on this area and she d ecided to seek a Masters degree on Coastal Engineering. After her graduation from collage in June 2005, she moved to Gainesville/Florida to obtain her Masters of Science degree in Coastal and Oceanographic Engineering from University of Florida.


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Permanent Link: http://ufdc.ufl.edu/UFE0017763/00001

Material Information

Title: Wave modifications in a semi-cnclosed basin: bahia concepcion
Physical Description: 68 p.
Language: English
Creator: Caliskan, Hande ( Dissertant )
Valle-Levinson, Arnoldo ( Thesis advisor )
Dean, Robert G. ( Reviewer )
Kennedy, Andrew B. ( Reviewer )
Sheremet, Alexandru ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Coastal and Oceanographic Engineering thesis, M.S   ( local )
Dissertations, Academic -- UF -- Civil and Coastal Engineering   ( local )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
theses   ( marcgt )
Spatial Coverage: United States -- California -- Bahia Concepcion

Notes

Abstract: In order to determine wave modifications in Bahia Concepcion, yearlong records of bottom pressure were obtained at the mouth and head of the bay. Wind waves were predominantly produced by southeastward winds in the winter and north-northwestward winds in the summer. Only 3, 7 and 15 second waves were recorded at the mouth of the bay, i.e. wave energy was produced only by 3, 7 and 15 second waves there. At the head of the bay 3 second waves dominated the wave energy. The energetic long-period swell waves were dissipated in the bay as they were not observed at the head of the bay. This study sought to identify the effects that caused the swell waves to attenuate in the bay. Numerical model results showed that long-period swell waves were attenuated because of the combined effects of bottom friction, refraction, diffraction and wave blocking. Most of the attenuation, however, was caused by wave blocking owing to the change of orientation of the bay.
Abstract: attenuation, Bahia, Concepcion, refraction, swan, swell
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 68 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0017763:00001

Permanent Link: http://ufdc.ufl.edu/UFE0017763/00001

Material Information

Title: Wave modifications in a semi-cnclosed basin: bahia concepcion
Physical Description: 68 p.
Language: English
Creator: Caliskan, Hande ( Dissertant )
Valle-Levinson, Arnoldo ( Thesis advisor )
Dean, Robert G. ( Reviewer )
Kennedy, Andrew B. ( Reviewer )
Sheremet, Alexandru ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Coastal and Oceanographic Engineering thesis, M.S   ( local )
Dissertations, Academic -- UF -- Civil and Coastal Engineering   ( local )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
theses   ( marcgt )
Spatial Coverage: United States -- California -- Bahia Concepcion

Notes

Abstract: In order to determine wave modifications in Bahia Concepcion, yearlong records of bottom pressure were obtained at the mouth and head of the bay. Wind waves were predominantly produced by southeastward winds in the winter and north-northwestward winds in the summer. Only 3, 7 and 15 second waves were recorded at the mouth of the bay, i.e. wave energy was produced only by 3, 7 and 15 second waves there. At the head of the bay 3 second waves dominated the wave energy. The energetic long-period swell waves were dissipated in the bay as they were not observed at the head of the bay. This study sought to identify the effects that caused the swell waves to attenuate in the bay. Numerical model results showed that long-period swell waves were attenuated because of the combined effects of bottom friction, refraction, diffraction and wave blocking. Most of the attenuation, however, was caused by wave blocking owing to the change of orientation of the bay.
Abstract: attenuation, Bahia, Concepcion, refraction, swan, swell
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 68 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

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WAVE MODIFICATIONS INT A SEMI-ENCLOSED BASIN:. BAHIA CONCEPCION


By

HANDE CALISKAN














A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA




2006
































Copyright 2006

by

Hande Caliskan









ACKNOWLEDGMENTS

I would like to thank to my advisor Arnoldo Valle-Levinson for his substantial help, moral

support and patience throughout this study, my committee members Robert G. Dean and Andrew

B. Kennedy for assisting me with their valuable knowledge, and Alexandru Sheremet for helping

me to find the suitable model for my study.

I also would like to thank to my wonderful parents, for their endless love and trust in me

and finally my friends for their incredible support.

Nothing would be as good as it is right now without you...












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............3.....


LIST OF TABLES .........__.. ..... .__. ...............5....


LI ST OF FIGURE S .............. ...............6.....


AB S TRAC T ......_ ................. ............_........8


CHAPTER


1 INTRODUCTION ................. ...............9.......... ......


2 METHODS ................. ...............11.......... .....


3 RE SULT S AND DI SCU SSION ............... ...............2


Observational Results ................. ...............22.......... .....
SWAN Wave Model Results ................ ...............24................


4 CONCLUSIONS .............. ...............66....


LIST OF REFERENCES ................. ...............67................


BIOGRAPHICAL SKETCH .............. ...............68....










LIST OF TABLES


Table page

2-1 CPU and wall-Clock times for three different grid sizes............... ...............21.

2-2 Test cases .............. ...............21....

3-1 Coordinates of the points where the frequency spectra is obtained ................. ................32

3-2 Coordinates of significant wave height ob servation points ................ ............ .........3 3

3-3 Percent reduction in significant wave height ................. ...............33........... ..

3-4 Differences in Hs and energy dissipation for the cases without bottom friction (Case
1); without bottom friction and depth induced wave breaking (Case 2); and without
bottom dissipation, depth induced wave breaking and whitecapping (Case 3). ................33

3-5 Percent reduction in energy per unit wave ray length due to combined effects of
bottom friction, depth-induced breaking and whitecapping; refraction and diffraction....33










LIST OF FIGURES


Figure page

2-1 B ahi a Concepci on and Measurement Stati ons ................. ....._.._......... .......1

2-2 Comparison of Contour Plots of Significant Wave Height for Available Friction
Model s in SWAN Wave Model ........._._.._......_.. ...............18...

2-3 Comparison of Contour Plots of Energy Dissipation for Available Friction Models
in SWAN Wave Model ........._._.._......_.. ...............19....

2-4 Contours of Significant Wave Height for Different Grid Sizes..........._.._.._ ........_.._.. ...20

3-1 Wave Energy Contours and Wind Velocity Vectors at ST1 between November 2004
and February 2005 .............. ...............34....

3-2 Wave Energy Contours and Wind Velocity Vectors at ST1 between February 2005
and April 2005 .............. ...............35....

3-3 Wave Energy Contours and Wind Velocity Vectors at ST1 between April 2005 and
June 2005 .............. ...............36....

3-4 Wave Energy Contours and Wind Velocity Vectors at ST1 between June 2005 and
August 2005 .............. ...............37....

3-5 Wave Energy Contours and Wind Velocity Vectors at ST1 between August 2005 and
November 2005 .........._. ..... ._ __ ...............38.......

3-6 Wave Energy Contours and Wind Velocity Vectors at ST2 between November 2004
and February 2005 .............. ...............39....

3-7 Wave Energy Contours and Wind Velocity Vectors at ST2 between February 2005
and April 2005 .............. ...............40....

3-8 Wave Energy Contours and Wind Velocity Vectors at ST2 between April 2005 and
June 2005 .............. ...............41....

3-9 Wave Energy Contours and Wind Velocity Vectors at ST2 between June 2005 and
August 2005 .............. ...............42....

3-10 Wave Energy Contours and Wind Velocity Vectors at ST2 between August 2005 and
November 2005 ........._._. ._......_.. ...............43.....

3-11 Graphical Representation of the Points where 1D Wave Spectra was Requested. ............44

3-12 Spatial Energy Density Contours in J/m2 for BC1, BC2 and BC3 .............. ..................45

3-13 Spatial Energy Density Contours in J/m2 for BC4, BC5 and BC6 ................. ...............46










3-14 Spatial Energy Density Contours in J/m2 for BC7, BC8 and BC9 ................. ...............47

3-15 Significant Wave Height Contours for BC1, BC2 and BC3 ................. ......................48

3-16 Significant Wave Height Contours for BC4, BC5 and BC6............... ...................4

3-17 Significant Wave Height Contours for BC7, BC8 and BC9............... ...................5

3-18 Mean Wave Direction Contours for BC1, BC2 and BC3 ................ ................ ...._.51

3-19 Mean Wave Direction Contours for BC4, BC5 and BC6 ........._.__........_ ..............52

3-20 Mean Wave Direction Contours for BC6, BC7 and BC8 ................ ................ ...._.53

3-21 Average Absolute Period Contours for BC1, BC2 and BC3 .............. ....................5

3 -22 Average Absolute Period Contours for BC4, BC5 and BC6............_ .........___.......55

3-23 Average Absolute Period Contours for BC7, BC8 and BC9 .......__........... ........ .......56

3 -24 Energy Dissipation Contours for BC1, BC2 and BC3 ................. ......... ................57

3-25 Energy Dissipation Contours for BC4, BC5 and BC6............... ...............58..

3-26 Energy Dissipation Contours for BC7, BC8 and BC9............... ...............59..

3-27 Spatial Energy Density Contours in J/m2 for BC2 and the Case without Bottom
Friction, Depth-Induced Breaking and Whitecapping ........._...__ ......._._ ........._.....60

3-28 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 2 and 25 m ...61

3-29 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 50 and 100
m .............. ...............62....

3-30 Spatial Energy Density Contours for BC2 and BC2 without Diffraction ................... .......63

3-31 Spatial Energy Density Contours for a Flat Bottomed Rectangular Bay with a Depth
of 100 m .............. ...............64....

3-32 Distance from the Mouth vs. Energy Density Plots for Cases BC2; BC2 without
Diffraction ........._._ ..... ._ ._ ..............65....









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science


WAVE MODIFICATIONS INT A SEMI-ENCLOSED BASIN:. BAHIA CONCEPCION

By

Hande Caliskan

December 2006

Chair: Arnoldo Valle-Levinson
Major: Coastal and Oceanographic Engineering

In order to determine wave climatology in Bahia Concepcion, yearlong records of bottom

pressure were obtained at the mouth and head of the bay. Wind waves were predominantly

produced by southeastward winds in the winter and north-northwestward winds in the summer.

Only 3, 7 and 15 second waves were recorded at the mouth of the bay, i.e. wave energy was

produced only by 3, 7 and 15 second waves there. At the head of the bay 3 second waves

dominated the wave energy. The energetic long-period swell waves were dissipated in the bay as

they were not observed at the head of the bay. This study sought to identify the effects that

caused the swell waves to attenuate in the bay. Numerical model results showed that long-period

swell waves were attenuated because of the combined effects of bottom friction, refraction,

diffraction and wave blocking. Most of the attenuation, however, was caused by wave blocking

owing to the change of orientation of the bay.









CHAPTER 1
INTTRODUCTION

Wave Climatology in semi-enclosed basins has been studied numerous times at different

sites all around the world. One of the common findings in these studies has been the observation

that ocean swell vanishes at some distances into the bay. For example, Boon et al., (1996)

observed that in Chesapeake Bay ocean swell waves were attenuated before they reach the

middle of the bay. Similarly, according to Long and Oltman-Shay's (1991) observation ocean

swell waves attenuated at the open coast of Duck, NC. According to their study in 1991, two

dimensional wave spectra were used at two different points, one of which was closer to the coast.

One of the observations was that wave frequency was higher and direction was nearly

perpendicular to the bottom contours at the point closest to the coast. At the offshore point,

frequency was lower and waves were propagating with a greater approach angle. This

observation has been used to hypothesize that the cause of the attenuation of ocean swell waves

was refraction. To my knowledge, this hypothesis has been the only attempt to explain the reason

for the attenuation of swell waves.

This study is motivated by the observation that low frequency waves (~ 7 s) were

dissipated in Bahia Concepcion, in the Gulf of California (Figure 2-1). In-situ data recorded at

two different stations suggested the influence of waves with periods of 5 7 s at the entrance but

waves with periods less than 5 s at the head. However, the main purpose of the data collection

was determining along-bay pressure gradients. Data were recorded according to the requirements

of the main purpose that might not have had appropriate temporal coverage to yield a reliable set

of data for wave climatology studies. In order to test the concept of wave attenuation in Bahia

Concepcion a numerical wave model, SWAN, was used first to be able to validate the reliability









of the data, secondly to find the possible reasons behind the attenuation and finally to show the

contribution of various dissipating effects on attenuation.

The study area is located on the Gulf of California side of the Baja California peninsula

between the longitudes of -1110 581 81 and -1110 401 61 and the latitudes of 260 32 211 and

26u 541 571 (Figure 2-1). Bahia Concepcion is exposed to strong winds from NW with a speed

more than 10 m/s for extended periods along its axis during the winter and spring seasons

(Badan-Dangon et al., 1991). Its bathymetry is quite simple. Immediately after the bay entrance,

there is a deep and narrow channel with an average depth of 30 m at the east side of the bay

mouth. The deepest point of the bay is located on this channel and the depth there is 34.5 m. The

bay entrance, with a width of 5.95 km, is located 39.98 km away from its south end point and the

bay width varies between 3.40 and 10.3 8 km. The west side of the bay, close to the mouth, has

the mildest bed slope causing an extended shallow zone from the coast. In this shallow zone,

between the latitudes of 26o 42' 3 1" and 26 o 45' 13 there are several islands. The names of the

islands are Isla San Ramon, Isla Pitahaya, Isla Blanca, Isla Bargo, Isla Guapa and Tecomate.

Semi-diurnal tidal height is observed to be 150 cm at the entrance and 36 cm at the head of

Gulf of California. The minimum semi-diurnal tidal height in the Gulf of California is observed

in its central regions with a value of 5 cm because of the existence of an semi-diurnal

amphidromic point. (Marinone et al., 2003). Since Concepcion bay is located at the Central Gulf

of California, tidal forcing along the bay is weak.









CHAPTER 2
METHOD S

In order to determine along-bay pressure gradient, bottom pressure was recorded every 15

min at the mouth and head of the bay (Figure 2-1). These measurements were obtained between

November 2004 and October 2005. Data were recorded with SBE26 instruments deployed at a

depth of 5.10 m at the mouth and 5.70 m at the head of the bay, below the mean sea level and

these stations are labeled as ST1 and ST2, respectively (Figure 2-1). In the mean time, wave data

were recorded with a frequency of 4 Hz at 30 s bursts every 3 hrs.

One of the most important inputs for determining the surface wave field is the wind data

because of its high contribution to wave development and growth. For this study, wind data

(wind velocity) were recorded using Aanderaa anemometers with a frequency of 1 Hz. For this

purpose instruments were installed 10 m above the mean sea level at the mouth and the head, at

distances less than 1 km from the bottom pressure recording stations, ST1 and ST2.

Although it was possible to measure wind waves with the available instruments, there was

no a-priori intention of resolving the wave field. Once again, the main purpose of the

deployment was to observe the pressure gradients along the bay. But in order to assess whether

the wind wave patterns observed were reliable, Concepcion Bay was modeled using the

Simulating Waves Nearshore Model (SWAN Model). The latest version available for public use,

SWAN Cycle III version 40.41, was used for this study.

Wave prediction models have been improved according to the improvements on the wave

evolution knowledge. First generation models did not consider nonlinear wave interactions while

second generation models included these interactions through some parameterizations. On the

other hand, third generation wave models used an explicit source term for non-linear wave

interactions (Hasselmann et al., 1985). SWAN is a third generation, numerical wave prediction









model that uses the known bathymetry, wind and current conditions for wave parameter

estimations. The model uses the wave action balance equation, which can be expressed in

Cartesian coordinates as (Hasselmann et al., 1973)

8N 83(cN) 8?(cN) 8?(c,N) 85(cHN)
-+ + + + = S,
dt Dx Sy 80 8

where N (c', 6) (= E(co, 6)/ co') is the action density, E(co, 6) is the wave energy density, co' is the

intrinsic frequency (i.e., frequency of wave components according to a reference moving with

the local current), t is time, ST is the source term, 6 is the wave direction and cx, c,, ce,, ce are the

propagation velocities in x, y, co' and 6 spaces, respectively. Each term of this equation can be

explained as follows:

8N
-Local rate of change of action density,




8 (cxN)
-Propagation of action in x direction,


83(c,,N)

"= Shifting of relative frequency due to depth and current variations,


8 (c, N)
-Refraction due to depth and current variations,


S, = Source term for wave energy growth due to wind, wave energy transfer due to nonlinear

wave-wave interactions and wave energy dissipation due to bottom friction, depth induced

breaking and whitecapping.

For this study, inputs to the model were bathymetry, wind velocity and wave forcing. A

southeastward wind of speed 10 m/s is used for the base case of the study because the bay is










exposed to southeastward winds with speeds exceeding 10 m/s for extended periods. In addition,

waves were prescribed from the N boundary with an approach angle of 300, a wave height of 1.5

m and a wave period of 10 s. The reason for prescribing waves with these parameters is to

represent the ocean swell waves entering the bay to be able to observe the changes that will

occur as they propagate towards the head. The outputs requested from the model were one

dimensional (frequency) spectra, significant wave height, mean wave direction, energy

dissipation, average absolute wave period and mean absolute wave period. For all tests, nonlinear

quadruplet wave interactions, depth induced wave breaking, whitecapping, bottom friction and

wind generation were activated to be able to obtain closer results to real life conditions.

SWAN has three optional formulations for friction calculations, which are:

* The empirical JONSWAP model (Hasselmann et al., 1973),

* Eddy viscosity model of Madsen et al. (1988),

* Drag law model of Collins (1972).

Using the available data it is not possible to make a calibration for bottom friction. Therefore, in

order to decide what friction formulation to use, a test was conducted. Three different cases were

run with the same boundary conditions, same southward wind of speed 10m/s. The only

parameter changed for these cases was the friction model. Although friction factors within each

formulation can be modified as required, default values were used for this test. Figures 2-2 and

2-3 show contour plots of significant wave height and energy dissipation over the bay for the

three friction models. According to the results obtained from this test, there was not much

difference in the general patterns of the contour plots. However, it was clear that the model of

Collins gave lower estimates of friction than both JONSWAP and Madsen's model. When the

models of Collins and Madsen were compared, it was seen that the greatest difference in energy

dissipation was 0. 1843 W/m2 at the mouth of the bay and was in the range of 0. 18 0.49 W/m2










along the breaker zone where most of the waves break. There is a ~20 m shoal at the mouth of

the bay between the longitudes of -1 1 1 52' 56" and -1 11 o 52' 12" and latitudes of 26o 51' 23 "

and 26 o 52' 41" (Figure 2-1). The depth decreases by 6 m at the bar and it is very likely that

waves feel the bottom and dissipate on it. The model of Collins gave low estimates for energy

dissipation over this bar and therefore JONSWAP and Madsen formulations were considered

further.

When JONSWAP and Madsen's models were compared it was seen that Madsen's model

gave greater energy dissipation values. The largest difference between the model estimates was

at the mouth, on the shoal, with a value of 0. 17 W/m2. Even though the dissipation estimates

were slightly different from each other, this only affected the significant wave height by 1.8cm.

Since this difference was very small when compared to the wave height it can be said that

Madsen's formulation produced consistent results with JONSWAP for this specific case.

According to the test results and knowing the fact that SWAN uses JONSWAP model as its

default setting, JONSWAP was chosen to be used in this study. Default values for the coefficient

of the JONSWAP formulation are: 0.038 m2/S3 for swell conditions and 0.067 m2/S3 for wind sea

conditions. In this study, both swell and local wind waves exist but SWAN does not have a

default value to consider both swell and wind sea conditions and with the available data it was

not possible to make a calibration for the JONSWAP formulation coeffcient. Therefore, both

coeffcients for swell and wind sea conditions were tested and it was observed that when the

coeffcient for swell conditions was used dissipation values were too small to be realistic and

therefore, 0.067 m2/S3 was used for the rest of the study.

Secondly, a sensitivity test for the model spatial resolution was conducted. The

computational grid that was used to generate results was determined using this sensitivity test.









For this test, three different grid sizes were selected for the same wind speed and direction to

observe the sensitivity of the calculations to the resolution. A southeastward wind with a speed

of 10 m/s (the predominant wind direction for the bay in winter), was selected to drive the model

with grid sizes of 100, 200 and 400 m both in the x and y axes. When compared to the finest grid

(100m), the 400m grid size was unable to resolve the details properly especially along the shore

due to inaccurate values obtained by interpolating a point inside the bay where the wave

parameters can be calculated and a point outside the bay where wave parameters cannot be

calculated. On the other hand, the grid size of 200m was able to resolve the bay better than 400m

showing enough details for the purpose of this study.

Figure 2-4 shows a comparison of these three grids for significant wave height

calculations. As the grid size increases, the model tends to overestimate the significant wave

height. The percent difference of significant wave heights between the grid sizes of 100m and

200m was less than 1% whereas between 100m and 400m, the difference increased to 4% along

the mid-span of the bay. Moreover, increasing the grid size made the model unable to resolve the

details along the shoreline. For example, using a grid size of 400m caused the islands, between

the longitudes of -1 1 1 54' 8" and -1 11 o 51' 43 and the latitudes of 26o 42' 31i" and 26 o 45' 13 ",

to disappear. On the other hand, a grid size of 200m was not only able to show enough details for

the purpose of the study, but also it saved a considerable amount of CPU and wall-clock time

(Table 2-1). The grid size of 200 m was chosen for the rest of the studies because it achieved the

required resolution and it saved a considerable amount of time for each run.

After determining the grid size, different cases for different wind speeds and directions

were run. The main purpose of these tests was

*to compare the behavior of waves at ST1 and ST2, where observations were available;










* to compare different model results with the available observational data;

* to observe the behavior of waves under different wind speed conditions; and

* to observe the differences due to different wind directions under a constant wind velocity.

First of all, the sensitivity of the wave parameters, such as significant wave height, wave

period and mean wave direction, to wind speed variability was tested with a fixed azimuth of

1500 and wind speeds of 5, 10 and 15 m/s. It should be noted that, here and throughout this

study, wind and wave directions will be presented according to oceanographic convention. In

other words, the direction where the wind is blowing (or the wave is propagating), is measured

clockwise from the North. Secondly, wind speed was kept constant at 10 m/s and variability of

the wave parameters as a result of the wind direction change was observed. All test cases are

summarized in Table 2-2.












26.9


STI


School


26.8

-30



I4




-50


26.7


















ST2




-111.95 -111.90 -111.B5 -111.80 -111.75 -111.70
LON
Figure 2-1 Bahia Concepcion and Measurement Stations

















Significant Wave Height (m)

MADSEN et al


COLLINS


JONS./1AP


25.9 26.9 26.9


26.85 ':B~ 26.85 ~ ~ ~ I 26.85





-8 26 75 26 75 -1' 26.75I







26.65 26 55 26.55



-111.9 -111.8 -111.7 -111.9 -111.8 -111.7 -111.9 -111.8 -111.7
Longitude (deg) Longitude (deg) Longitude (deg)


O 0.2 0.4 0.5 O 8 1 1.2 1.4 1 6 1 8

Figure 2-2 Comparison of Contour Plots of Significant Wave Height for Available Friction Models in SWAN Wave Model

















Energy Dissipation (W/rn )

COLLINSMADSEN et al. JONSWAP

26926.9~`1 26.9


26.85~ 26.85 26.85


26.8 F L26 8 26.8



26.75 26.75 26.75



26.65 C 1 26.65 26 65


26.6 C 126.6 26.6

2.526.55 r8 26 55
-1119 -11.8-11 7 111.9 -111.8 -111.7 -111 9 -111.8 -111.7
Longitude (deg) Longitude (deg) Longitude (deg)


O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure 2-3 Comparison of Contour Plots of Energy Dissipation for Available Friction Models in SWAN Wave Model
































I 1 1


(a) Grid size=100~m


(b) Grid size=200m


(c) Grid size=400m
26.9

26.85

S26.8

as26.75

26.7 t

S2.526.65 L P

26.6

26.55
-111.95 -111.85 -111.75
Longitude (deg)


26.9

26.85


268
26.75

S26.7

S26.65 -

26.6 .

26.55 ,
-111.95 -111.85 -111.75
Longitude (deg)


26.9

26.85 ,

S26.8

~26.75

S26.7

S26.65

26.6 .

26.55 ,,
-111.95 -111.85 -111.75
Longitude (deg)


Figure 2-4 Contours of Significant Wave Height for Different Grid Sizes











Table 2-1 CPU and wall-Clock times for three different grid sizes
Grid Size (m) 100 200 400

Total CPU Time 7029.81 1725.39 394.98

Total Wall-Clock Time (s) 46240.12 1871.61 413.74


Wind Wind
Name of
thease Speed Direction
(m/s) (o>
BC1 5 150

BC2 10 150

BC3 15 150

BC4 10 180

BC5 10 120

BC6 10 50

BC7 10 20

BC8 10 90

BC9 10 0


Table 2-2 Test cases









CHAPTER 3
RESULTS AND DISCUSSION

This chapter contains two sections. In the first section of this chapter, results derived from

the data collected by the bottom mounted instruments will be presented. The second section

includes the detailed model results and a comparison of them with the observational results.

Observational Results

As mentioned before, wind velocity data were recorded at ST1 and ST2 with a frequency

of 1 Hz. To be able to eliminate high frequencies in the wind data, Lanczos filter, which is a

low-pass digital filter, was used. Then wind velocity vectors are decimated and plotted for every

3 hrs over the full deployment duration at the mouth (Figures 3-1b 3-5b) and at the head

(Figures 3-6b 3-10b). In these plots, direction of the vectors demonstrates where the wind is

blowing to and magnitude of the vectors demonstrates its speed. The scale for the speed is shown

on the y-axis in m/s. It should also be noted that there were missing data due to recording

problems, especially at the mouth of the bay. These periods are marked with a horizontal dashed

line plotted at zero velocity to differentiate the recording durations.

Figures 3-la 3-10a show contours of wave energy, plotted in time and frequency space.

As a matter of fact, in these plots, each section cut vertically would represent the wave spectrum

of a burst that was recorded at the time of the selected section. The reason for plotting these

wavelets was to give a better representation of the observed wave energy with different

frequencies over the full deployment duration. Energy (in cm2) here is defined to be the sum of

the variances over each frequency band. For example, contours plotted for a wave period of 7 s

show the sum of the variances for the frequencies between 1/8 and 1/6 Hz.

Figures 3-la 3-10a and 3-1b 3-10b are presented for the same periods of time and

plotted one on another to be able to show the high correlation between wind velocity and wave










action. As the data suggest, when wind speed increases, wave action usually increases too.

However, for the cases of strong eastward or westward winds, it is not possible to observe this

correlation. The main reason for this weak correlation is the short fetch in the east west

direction. The data suggest that wave action in the bay is highly correlated with the speed of

winds blowing along the axis of the bay (winds from NW NE) because of its longer fetch that

allows waves to grow.

Contour plots at the mouth of the bay (Figures 3-la 3-5a) show that wave energy is

mostly concentrated on 3-7 s waves and it is possible to observe some energy on 13-15 s waves.

However, in reality more energy could be concentrated on low frequency waves (i.e. periods of

13-15 s or more). It is not possible to observe this with the available data because each burst

consisted of a 30 s recording interval. Such an interval may not be enough to capture enough

number of low frequency waves to be able to show the actual energy they have.

On the other hand, the data set for the head of the bay shows that wave energy has

decreased considerably although wind speed has not decreased more than 20%. For instance, 13-

15 s waves have completely disappeared, it is not possible to observe as much energy on 5-7 s

waves as at the mouth and even the energy on 3 s waves that can be produced by local winds has

decreased considerably. (Figures 3-1b 3-5b)

The reduced wave activity at the head of the bay is either caused by transfer or by loss of

wave energy and the reasons for that might be refraction, shoaling, bottom friction, whitecapping

or any combination thereof. To see if the computational model will give similar results to what

has been observed and to be able to understand the reasons of low frequency wave attenuation at

the head, the SWAN wave model has been run and results obtained are presented in the

following section.









SWAN Wave Model Results

Figures 3-12, 3-13 and 3-14 show the spectral energy density distributions in J/m2/Hz

derived from the SPEC1D command of SWAN model, which gives the one-dimensional spectra,

for all of the test cases presented in Table 2-2. These contours were plotted for the frequency

range 0.05-0.5 Hz using the spectra that were obtained at 20 different points selected

approximately in the middle of the bay from mouth to head. Coordinates of the selected points

are presented in Table 3-1 and locations are shown in Figure 3-11 with a star. The ordinate axis

of the contour plots show the distances from the head in meters meaning that the zero point

shows the mouth of the bay.

All contours, regardless of wind speed and direction, show that the bay has a behavior of

attenuating the highly energetic long waves as they propagate toward the head. It is possible to

see that approximately around 15 km from the mouth most of the low frequency waves were

dissipated in all cases. On the other hand, higher frequency waves exist everywhere along the

bay. This behavior was also one suggested by the field data. Therefore, model results suggest

that observational data presented in the previous section have a revealing pattern of the wave

behavior in the bay.

As mentioned previously, BC1, BC2 and BC3 cases were run to see the response of the

bay to wind speed change under the same wind direction and wave forcing conditions. Energy

density contours of these cases are presented in Figure 3-12. One of the maj or differences in

these three plots is the frequency range of waves at the head of the bay. It is seen that the

frequency range at the head of the bay increases as the wind speed increases. For BC1, wind

speed is 5 m/s and the frequency of most of the waves reaching the head ranges between 0.28

and 0.50 Hz, giving a range interval of 0.22 Hz. For BC2 where the wind speed is 10 m/s this

range is between 0.18 and 0.50 Hz causing the interval to increase to 0.32 Hz. The frequency










range for BC3 (wind speed = 15 m/s) is between 0.14 and 0.50 Hz and the range interval is 0.36

Hz. This suggests that stronger winds can generate waves with a wider range of frequencies

when compared to weaker winds.

The response of the bay to the wind direction change is displayed by the energy density

contours for BC2 and the cases BC4 BC7 (Figures 3-12, 3-13, 3-14). When the bay is under the

effect of southward southeastward winds, (Figures 3-12 and 3-13 for BC2, BC4 and BC5)

energy contours were very similar to each other. In other words, even adverse winds did not

affect the distance traveled by the swell waves. The only difference observed was at the locally

generated short wind waves.

When the wind was blowing from between west and south; the distance, along which the

low frequency waves attenuated, was equal to the distance for cases BC2, BC4 and BC5.

However, the frequency of the waves that reached the head of the bay decreased considerably.

This is due to the effect of the adverse wind and the direction the prescribed waves at the mouth

of the bay. Since the wind was blowing from the opposite direction, waves were dissipated as

they propagated towards the head. This caused the frequency of the waves that were able to

reach to the head to further decrease. (Mitsuyasu, 1997)

As stated previously, attenuation of low frequency waves was observed from the in-situ

data and the SWAN model was used to verify the reliability of the observational results. Since

the model results verified that the observational results were reliable, the SWAN model results

were also used to determine the reasons for attenuation of the low frequency waves as they

propagated towards the head. As mentioned before, significant wave height, mean wave

direction, average wave period and energy dissipation outputs were requested from the model.









These parameters are presented in contour maps and used both for reinforcing the observational

results and finding a reasonable explanation to what has been observed (Figures 3-15 3-26).

Significant wave height (Hs) contour maps show that for all cases, Hs decreases

considerably from the mouth to a distance of 6 km into the bay (Figures 3-15 3-17). This

attenuation mainly occurs on the west side of the bay entrance. The 30 m deep channel on the

east side of the mouth does not have a significant effect on Hs attenuation. Further into the bay,

Hs increases slightly for the case of southward and southeastward winds (for cases BC2, BC3

and BC5) because the wind causes waves to grow along the longest fetch in the bay. Although

the wind direction for BC1 (wind speed = 5 m/s) is the same as BC2, BC3 and BC5, there is a

decrease in Hs. This indicates that when the wind is not strong enough, its growing effects on

waves is not enough to overcome the attenuating effects such as refraction, diffraction and

bottom friction. When the wind is blowing from other directions than between N and NW, Hs

continues to decrease as the waves propagate towards the head. For cases BC7 and BC9 even

after passing the narrow channel close to the mouth of the bay, Hs attenuation continues at a

higher rate than other cases. This is caused by the dissipation effect of the opposite directions of

the wind and wave propagation. To see the percent reduction in the Hs three different points are

selected, one at the mouth of the bay, one after the dissipative channel and one at the head of the

bay. Table 3-2 and Table 3-3 show the coordinates of these points and the percent reduction in

the significant wave height relative to the point at the mouth, respectively.

For BC1, BC2 and BC3 significant wave height maps show an increase in Hs pattern all

over the bay as the wind speed increases from BC1 to BC3 (Figure 3-15). This indicates the well

known wave behavior that the wind speed has a direct effect on wave generation and wave

growth (Jeffreys, 1924). When the contour maps for the rest of the cases are observed, the first









difference one can notice is the locations of the areas where the Hs is less than 0.2 m (Figures 3-

16 and 3-17). These calm areas exist if the wind direction is not aligned with the swell

propagation direction and their locations depend mainly on the magnitude of the 'y' component

of the wind. If the 'y' component dominates the wind as in cases BC7 and BC9, a low energy

area is located at the SW whereas if the east component starts to dominate, this area elongates

towards the NW into the islands.

Figures 3-18, 3-19 and 3-20 show mean wave direction contours that reveal the patterns of

refraction. By looking at these contour maps it can be said that this final version of SWAN can

predict refraction quite well even around the islands to the south of the latitude 260 421 36 1. Since

it has been observed that the SWAN wave model is capable of calculating the refraction, the

contribution of the refraction to the low frequency wave attenuation will be presented in the

following sections of this chapter.

Dense contours at the mouth of the bay and along the channel in average absolute wave

period contour maps (Figures 3-21, 3-22, 3-23) clearly show the attenuation of low frequency

waves. At the deep channel on the east side (immediately south of the bay entrance) the wave

period change is not as large as it is on the west side. This may suggest that the swell attenuation

is related to the depth and this will be investigated in the following sections of this chapter.

Energy dissipation (W/m2) COntour maps illustrate the sum of various processes: depth

induced wave breaking, bottom friction and whitecapping (Figures 3-24, 3-25, 3-26). From these

plots, it is clearly seen that a relevant cause of significant wave height attenuation and average

mean period maps is energy dissipation. It is possible to see the high correspondence of energy

dissipation with Hs and average mean period especially at the locations where strong attenuation

occurs. For example, at the bay entrance, where water depth decreases by 6 m, it is possible to









observe higher rates of energy dissipation and significant wave height. It should also be noted

that the reduction in the depth here may also have a contribution to the swell attenuation.

After determination of the correspondence between energy dissipation and significant

wave height attenuation, three more cases were run to observe the effect of bottom friction, wave

induced breaking and whitecapping to the significant wave height and the wave spectra. New

cases were generated by changing the dissipation formulations of the base case, BC2, without

changing the bathymetry, wave and wind conditions. In the first case bottom friction was

reduced by introducing a very small coefficient into the JONSWAP formulation ([cfj on] =

0.0001 m2/S3) to be able to see the contribution of bottom friction to the low frequency wave

attenuation. For the second case the coefficient of JONSWAP formulation was kept at 0.0001

m2/S3 and in the mean time, the depth-induced wave breaking option of SWAN was turned off.

Finally, for the third case whitecapping was turned off in addition to the conditions in case 2.

These three cases were compared with the base case, BC2, and the maximum differences of

significant wave height and energy dissipation between the new cases and BC2 are displayed in

Table 3-4. These results showed that the greatest difference occurred at the shallow section of the

bay entrance (especially over the sand bar). The most significant contribution to energy

dissipation was from bottom friction with a value of 16.636 W/m2 and this caused the highest

attenuation in Hs with a value of 3.02 m. According to the results presented in Table 3-4 depth-

induced wave breaking and whitecapping do not have a significant effect on the energy

dissipation. As a matter of fact it is possible to see the greatest effects of depth-induced breaking

at the breaking zone. However, for the purpose of this study data at the breaking zone was not

examined. Although it was possible to observe the differences in energy dissipation and Hs due

to bottom friction, depth-induced wave breaking and whitecapping separately, Figure 3-27









shows that these factors do not affect the wave spectra significantly. It only shows the spectra for

the base case, BC2, and the case without bottom friction, depth-induced wave breaking and

whitecapping. Even in this case, the spectra for these cases are almost identical and this suggests

that attenuation (or energy dissipation) of the waves as they propagate towards the head is not

greatly affected by bottom friction, depth-induced breaking or whitecapping.


The previous test showed that the attenuation of the low frequency waves was not affected

significantly by the components of energy dissipation. Additional reasons for the low frequency

waves to attenuate can be the refraction and shoaling. Since both refraction and shoaling are

depth-dependent occurrences, some changes were made on the bathymetry fie to observe the

change in the behavior of the low frequency waves. For this purpose, three new cases were run

with a wind velocity and wave forcing the same as the base case, BC2, but with flat bathymetries

of depths 2, 25, 50 and 100 m. It should be noted that the JONSWAP friction coefficient, depth-

induced breaking and whitecapping options were not changed or turned off for the new cases.

Depths were chosen to be able to observe the behavior of the bay in shallow, intermediate and

deep water conditions. Waves can be categorized as shallow water waves, intermediate depth

waves and deep water waves according to the following conditions (Dean and Dalrymple, 1991):



(k) Shallow Water Waves


(kh) < x Intermediate Depth Waves


(kh) < li Deep Water Waves


where k is the wave number and h is the water depth.









Using these conditions, a wave period of 10 s (wave period selected for model calculations) and

the dispersion relationship, r2 = (gk)tanh(kh) where g is the gravitational acceleration, one can

obtain the depths separating shallow water from intermediate depth and intermediate depth from

deep water. These depths were found to be 2.38 and 77.87 m, respectively. Figures 3-28 and 3-

29 show the one dimensional wave spectra for these cases. The plot for 2 m represents shallow

water waves, plots for 25 and 50 m represent intermediate depth and 100 m represents deep

water conditions. From these figures it is possible to observe that low frequency waves can

propagate further into the bay as the water depth increases (i.e. as the waves propagate in deeper

water). For instance, for shallow water (depth of 2 m), 10 s waves cannot be observed after 500

m into the bay from the mouth, but for intermediate depths of 25 and 50 m, it is possible to

observe them up to 20 km. On the other hand one may expect to observe low frequency waves

further into the bay for the deep water case. However, model results showed that even for a depth

of 100 m low frequency waves disappeared 22 km before reaching the head. Because

bathymetric effects were eliminated by introducing a flat bottom, and hence refraction effects

were suppressed, one possible reason for the wave dissipation was the geometry of the bay. The

bay did not have a straight geometry causing waves to be blocked as they propagate, especially

at latitudes 260 421 361 and 260 461 48 1. At locations where the propagation of low frequency

waves was blocked, energy was distributed laterally, perpendicular to the dominant wave

direction and thus waves attenuated. This phenomenon is called wave diffraction (Dean and

Dalrymple, 1991). The version of SWAN that was used for this study has the ability to consider

the effects of diffraction and in this particular case, since the bathymetric effects were

eliminated, it may be possible to observe diffraction effects. However, since diffraction is more

effective in small-scale models, one other case was added to verify the effects of diffraction. In









this case diffraction was eliminated from the base case, BC2, and wave spectra are presented in

Figure 3-30. As the figures suggest, diffraction affects swell waves at the mouth of the bay where

dimensions are relatively smaller than the rest of the bay. However, its effect decreases as the

waves propagate into the bay and hence it is not possible to observe swell waves beyond 16 km.

Since it is not possible to observe swell waves at the head of the bay even after eliminating

bottom friction, refraction and diffraction, one final case is added to be able to observe the effect

of bay geometry. In this case, the bay geometry was replaced by a rectangle with a width of 7 km

and a length of 42 km. Once again a flat bottom in deep water conditions (100 m) was selected

and waves were prescribed to propagate southward from the north boundary of the bay with a

wave height of 1.5 m and wave period of 10 s. Wave propagation direction was changed for this

case to be able to make the propagation direction perpendicular to the bottom contours. In

addition to these, bottom friction was reduced once again by assigning the coefficient of

JONSWAP to be 0.0001 m2/S3. Figure 3-31 shows the wave spectra for this case and as it can be

observed from the figure, some low frequency waves were able to propagate from the mouth to

the head without attenuation.

Figure 3-32 shows the distribution of the wave spectra along the distance from the bay

mouth to the head, at a wave frequency of 0. 1 Hz for the cases BC2; BC2 without bottom

friction, depth-induced breaking and whitecapping; flat bottom with a water depth of 100 m; and

rectangular bay without bottom friction, depth-induced breaking and whitecapping. With the

original bay geometry, even for the most basic case where bottom friction, depth-induced

breaking, whitecapping, refraction and diffraction were eliminated, energy density curve

decreases from mouth to the head. However, when bay is replaced with a rectangle with the same

dimensions, wave energy kept constant. This shows that most of the swell waves could not reach


































7769.3599 41578.6016
8584.3398 39341.1992
9562.3301 36637.6992
10540.2998 33561.1992
11681.2998 31417.0000
12278.9004 29366.0000
12604.9004 27315.0000
12713.5996 25543.6992
13039.5996 22747.0000
13256.9004 20416.3008
14180.5996 18458.5000
14886.9004 16966.9004
15484.5996 15195.5996
16625.5000 13610.7998
17657.9004 12305.5996
18472.8008 10441.0996
19831.0996 8483.3398
21352.5000 6432.3701
22765.0996 4101.7100
24014.6992 1491.3800


the head of the bay because of the blocking effect of the land. In addition, it has been observed

that diffraction, bottom friction, whitecapping and depth-induced breaking have very small

contribution to swell attenuation. Refraction has the most contribution to the swell attenuation,

especially close to the bay mouth where waves had not been blocked by the land. The

contributions of refraction, diffraction and the combined effect of bottom friction, whitecapping

and depth-induced breaking were calculated from the areas under the energy density curves and

are represented in Table 3-5. This table shows most of the contribution to the swell attenuation is

caused by refraction close to the mouth and the effect of diffraction, bottom friction, depth-

induced breaking and whitecapping is negligibly small.


Table 3-1 Coordinates of the points where the frequency spectra is obtained


X Coordinate (m)


Y Coordinate (m)










Table 3-2 Coordinates of significant wave height observation points
Point at the Mouth Point after the channel Point at the head
Longitude -111.8781 -111.8398 -111.7208
Latitude 26.8835 26.7807 26.5608


Table 3-3 Percent reduction in signfcant wave heigh
% REDUCTION IN
SIGNIFICANT WAVE HEIGHT
Test Cases Point after the Point at the
channel head
BC1 70.53 72.80
BC2 43.62 39.32
BC3 31.88 20.76
BC4 47.71 47.95
BC5 53.64 45.71
BC6 57.97 60.01
BC7 52.59 91.49
BC8 52.60 58.23
BC9 48.33 94.64


Table 3-4 Differences in Hs and energy dissipation for the cases without bottom friction (Case 1);
without bottom friction and depth induced wave breaking (Case 2); and without
bottom dissipation, depth induced wave breaking and whitecapping (Case 3).
Difference Between Max. Difference in Energy Max. Difference in Hs (m)
Dissipation (W/m2)
Case 1 and BC2 16.621 3.020
Case 2 and BC2 16.636 3.051
Case 3 and BC2 16.639 3.069


Table 3-5 Percent reduction in energy per unit wave ray length due to combined effects of
bottom friction, depth-induced breaking and whitecapping; refraction and diffraction.
Attenuation due to % Reduction in Eney
Refraction 14
Combined effect of bottom friction, < 1
depth-induced breaking and whitecapping
Diffraction < 1
Blocking. of land 84






































































O




-2




4




-6




8


Dec


._an


Feb


Figure 3-1 Wave Energy Contours and Wind Velocity Vectors at ST1 between November 2004 and February 2005

















Oi i 0 01


Wli


. .


I


I


rII m I I I in m l


14


10


8


1~1


F r h


0..1r


O


-8 -


10


F ib


Eselar


Figure 3-2 Wave Energy Contours and Wind Velocity Vectors at ST1 between February 2005 and April 2005


UY WYW


WIY U


~














~ W WVU Y YYW Y U YWUVYYIW WWIIVW YYY' YW YY W YWW














Y~IY ai~ IM


.pr


Mv1a y


WW WY WKW ~W.Iher U


O 1


4

6

-8

10
Apr


Jun


Figure 3-3 Wave Energy Contours and Wind Velocity Vectors at ST1 between April 2005 and June 2005







































































Figure 3-4 Wave Energy Contours and Wind Velocity Vectors at ST1 between June 2005 and August 2005


O


2


14


"'~T Iri~ ~P"


Jul


Aug


Sep

















14


10



8



6



4 I1P IKVRII[ 1Y W1 lllh iol,~l(lVIIIVIILI


Sep Oot Nov


4

W
00 i

j


o ~X~b~,,

E
r





B



8



io
~ep Oct Nov


Figure 3-5 Wave Energy Contours and Wind Velocity Vectors at ST1 between August 2005 and November 2005

























9



T 1


1~1


ae~


Jan


Feb


lec


Jarl


Feb


Figure 3-6 Wave Energy Contours and Wind Velocity Vectors at ST2 between November 2004 and February 2005
































































Figure 3-7 Wave Energy Contours and Wind Velocity Vectors at ST2 between February 2005 and April 2005


Ils$ig~~lh~,hhl~~lQA1Bi hl~B118lhhlh~ln MhlhPlhOmrB~1


11-1 -~1-111111 11 II 111 111 1 111 11-1 11 11-11-- 1111111111-1111 -(il-lll II --I- 11 I -~II- -1 ~-


13


11


Feb


[var


Feb


[var


























h ~ Ir h it


~R~


111


1~1


sC


[vay


.hir


v1a y


.J :.1r


Figure 3-8 Wave Energy Contours and Wind Velocity Vectors at ST2 between April 2005 and June 2005


hff3RIWiBB rll$QMBnh IlhlhBhk. Ilih In





1~1


sC


dll I


Mhl
Au,


I Ihlh


II h


II Ih~lJul


01


Aug


Figure 3-9 Wave Energy Contours and Wind Velocity Vectors at ST2 between June 2005 and August 2005


r I hk hh IC























11













































- E.








.Au e Oc





Fiue 31 aeEeg otusadWn eoiyVcosa T ewe uut20 n oebr20
















i


26.9 t


2B.85-





2B.8-








26.75








26.65-





2B.6-





26.5 -

-111.95 -111.9 -111.85 -111.8 -111.75 -111.7

Longitude if)


Figure 3-11 Graphical Representation of the Points where 1D Wave Spectra was Requested















x 10- BC1 x 10
E 4r v


E 4.5
E2--
L-4



0.05 O 1 0.15 0.2 0.25 0 3 O 35 O 4 O 45 0.5
Frequency (Hz )

4r
x 0 C
4 II-













S0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 4 O 45 0.5
Frequency (Hz ) C1.


Figure 3-12 Spatial Energy Density Contours in J/m2 for BC1, BC2 and BC3















4


E 4


LL
~1


0.05


4
4r








P~ WP





S0.05


4,


0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Frequency (Hz )
BC5


U.1b


Frequency (Hz )
BCB


U.1b


Frequency (Hz )


Figure 3-13 Spatial Energy Density Contours in J/m2 for BC4, BC5 and BC6













































Figure 3-14 Spatial Energy Density Contours in J/m2 for BC7, BC8 and BC9


Sx10






S0.05


4




LL ,


0.05

4
x 10

4r,



S0.05


x10


0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Frequency (Hz )
BCB


0.5


U.1b


Frequency (Hz )


Frequency (Hz )


















Significant Wave Height (m)

BC1 BC2 BC3

26.9C 2B.9 26.9


26 BSt 26.85 +1 26.85





S26 75 -m 26.75 26 75 1

26.7 26.7 -, .26.7


26.65 C 1 2B.B5 26 65




26 55 C 1 26.55 26.55
-111 9 -111 B -111.7 -111.9 -111.8 -111.7 -111.9 -111.8 -111.7
Longitude (deg) Longitude (deg) Longitude (deg)



0 0.2 0.4 0.B 0.8 1 1 .2 1 .4 1 .B

Figure 3-15 Significant Wave Height Contours for BC1, BC2 and BC3

















Significant Wave Height (rn)


BC4 BCS BCB

26.9C 2B.9C 26.9


26 BS 26.85 .C 26.85



26 75 26.75 26 75

I .-
26 75 2B.7 26 7 '



26 B 26.65 26.6
26.B -2B.B 26.B


26 655 65 26.55



-111 9 -111 8 -111.7 -111.9 -111.8 -111.7 -111.9 -111.8 -111.7
Longitude (deg) Longitude (deg) Longitude (deg)


O 0.2 0.4 0.6 0.8 1 1.2 1 .4 1.B 1.8


Figure 3-16 Significant Wave Height Contours for BC4, BC5 and BC6

























































0 0.2 0.4 0.6 0.B 1 1.2 1.4 1.6 1 .8


Figure 3-17 Significant Wave Height Contours for BC7, BC8 and BC9


Significant Wave Height (m)


BCB


26.85


2B.B




2B.75




26.65


2B.B


26.55


h

v

a
ul ~
o


-111 9 -111 8
Longitude (deg)


-111 7


-111.9 -111.8 -111.7 -111.9 -111.8 -111.7
Longitude (deg) Longitude (deg)




















BC2








-3 1


-111.9 -111.8 -111.7
Longitude (deg)


200 250 300 30


200 250 300 350


Mean Wave Direction (O


S26.75


26 75


2B BS









26.55


26.85~


S26.75


5 2 7


2B.B5


26 6 1


,-
2


26.55 C


-111.9 -111.B
Longitude (deg)


-111 7


111.9 -111.8
Longitude (deg)


-111.7


200 250


300 350


Figure 3-18 Mean Wave Direction Contours for BC1, BC2 and BC3



















































200 250 300 350


200 250 300 350


0 100 200 300


Mean Wave Direction (O


BCS


I.L
I '


2B 85





26.75








26.6


2B.85


26 8 ~


-0 26.75
26


t.-


2B.B5 E


2B B E


-111.9 -111.8
Longitude (deg)


26.55


26.55


111.7


-111.9 -111.B
Longitude (deg)


-111 7


111.9


-111.8
Longitude (deg)


-111.7


Figure 3-19 Mean Wave Direction Contours for BC4, BC5 and BC6


















































O 100 200 300


0 100 200 300


200 250 300 350


Mean Wave Direction (O


BCB


26.9 -


26.85 -


26.B -


0 26.75 -


S26.7 -


26.65 .


2B.B .


26.55 -


26.9


2B.B6


26.8


26.75


2B 7


2B.B5


2B B


2B.55


26.9


2B 85


26 B


26.75


26 7


2B BS


26.6


26.55


-111.9 -111.8
Longitude (deg)


- 1.


111.7


-111.9 -111.B
Longitude (deg)


-111 7


111.9 -111.8
Longitude (deg)


Figure 3-20 Mean Wave Direction Contours for BC6, BC7 and BC8


















































O 1 2 3 4 5 B 7 B G


Figure 3-21 Average Absolute Period Contours for BC1, BC2 and BC3


Average Absolute Period (s)

BC2 BC3


26.9


26.85


26.8


26 75


26.7


26 BS


26.6


26 55


26.9


26 BS


26 B


26 75


26 7


26.65


26.6


26.55


2B.9


2B.B5


2B.B


2B.75


2B.7


26.65


2B.B


26.55


- 1.


111.9 -111.8
Longitude (deg)


111.7


-111.9 -111.B
Longitude (deg)


-111 7


-111.9 -111.8
Longitude (deg)

















































O 1 2 3 4 5 B 7 B


Figure 3-22 Average Absolute Period Contours for BC4, BC5 and BC6


Average Absolute Penod (s)

BCS


2B.9













26.65




26.55


26.65


26.6


26.55


111.9 -111.8 -111.7
Longitude (deg)


-111.9 -111.B
Longitude (deg)


-111 7


-111.9 -111.8
Longitude (deg)


-111.7




















































O 1 2 3 4 5 6 7 B


Figure 3-23 Average Absolute Period Contours for BC7, BC8 and BC9


Average Absolute Period (s)

BCB


26.9


26.85


26.8


26.75


26 7


26.65


26.6


26.55


26.9


26 85


26.8


26 75


26.7


26.65


26.6


26.55


-111 9 -111.8
Longitude (deg)


-111.7


-111.8
Longitude (deg)


-111.9 -111.8 -111 7
Longitude (deg)



















































I O 05 0.1 0.15 0 2 O 25 D.

Figure 3-24 Energy Dissipation Contours for BC1, BC2 and BC3


Energy Dissipation (W/rn )

BC2


26.9


26.85


26.8


26 75


26.7


26 BS


26.6


26 55


26.9


26 BS


26 B


26 75


26 7


26.65


26.6


26.55


2B.9


2B.B5


2B.B


2B.75


2B.7


26.65


2B.B


26.55


-111.9 -111.8
Longitude (deg)


111.7


I
-111.7


-111.9 -111.B
Longitude (deg)


-111 7


-111.9 -111.8
Longitude (deg)











































I I I


0 0.05 0.1 0.15 0.2 0.25 0.

Figure 3-25 Energy Dissipation Contours for BC4, BC5 and BC6


Energy Dissipation (W/rn )

BCS


26 9


26.85


26.8


0 26.75


26.7


00 26.65


26 B


26 9


26 BS


26 B


26.75


26 7


26 BS


26 B


26.55


26.9


2B.B5


2B.B


26.75


2B.7


2B.B5


2B.B


26.55


-111.9 -111.B
Longitude (deg)


-111.9 -111.8
Longitude (deg)


111.7


111.9 -111.8
Longitude (deg)


-111.7


















































O 0.05 0 1 0 15 0.2 0.25 0


Figure 3-26 Energy Dissipation Contours for BC7, BC8 and BC9


Energy Dissipation (W/rn )

BCB


26.9


26.85


26.8


26 75


26.7


26 BS


26.6


26 55


26.9


26 BS


26 B


26 75


26 7


26.65


26.6


26.55


2B.9


2B.B5


2B.B


2B.75


2B.7


26.65


2B.B


26.55


-111.9 -111.B
Longitude (deg)


- -


111.9 -111.8
Longitude (deg)


111.7


-111.9 -111.8
Longitude (deg)













BC2


x 10


3.5 _

S3-

S2.5- /


1.-/

a9 1 5




0.05


x 10

45


35
S3




1.5
1
0.5






x 10


0.25 0.:
Frequency (Hz.)


BC2 without bottom friction, depth-induced breaking and hiltecapping


x 10


3.5-

3-

2.5-






0.5

0.05


0.25 0.:
Frequency (Hz.)


Figure 3-27 Spatial Energy Density Contours in J/m2 for BC2 and the Case without Bottom Friction, Depth-Induced Breaking and
Whitecapping



































0.25 0.3 0.35 0.4 0.45
Frequency (Hz.)


L.L
-1.5



0.5

0.05


0.25 0 3
Frequency (Hz)


Figure 3-28 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 2 and 25 m
























S2.5


LL.
8 1.5

-~C 1


0.25 0.3
Frequency (Hz.)


h=100rn


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Frequency (Hz.)

Figure 3-29 Spatial Energy Density Contours in J/m2 for Flat Bottoms with Depths of 50 and 100 m













x 10' BC2 : 10






11 -





0.5 -_ _

0.05 0.1 0.15 0 2 0.25 0.3 0.35 0 4 0.45 0.5
Frequency (Hz )



x 10' BC2 wYithout Diffraction


35-











05i III
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (Hz.)



Figure 3-30 Spatial Energy Density Contours for BC2 and BC2 without Diffraction











Spatial Energy Density (J/m2)


x 10





3.5


1


~ I I


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Frequency (Hz)

Figure 3-31 Spatial Energy Density Contours for a Flat Bottomed Rectangular Bay with a Depth of 100 m













-- BC2
-9 BC2 wYithout Diffraction
-9- BC2 wiithout Diffraction, Bottom Friction, Depth-Induced Breaking and Whitecapping
SFlat Bottom with a Depth of 100 m
Rectangular Bay


O 0.5 1 1 .5 2 2.5 3 3.5 4 4.5
Distance From The Mouth (m) x 104

Figure 3-32 Distance from the Mouth vs. Energy Density Plots for Cases BC2; BC2 without Diffraction, BC2 without Diffraction,
Bottom Friction, Depth-Induced Breaking and Whitecapping; Flat Bottom for Deep Water Conditions (Depth=100m) and
Rectangular Bay without Diffraction, Bottom Friction, Depth-Induced Breaking and Whitecapping









CHAPTER 4
CONCLUSIONS

It has been observed both from the in-situ data and model results that the ocean swell

waves were attenuated as they propagate into the bay and before reaching the head they

completely disappeared. Moreover it was possible to observe locally generated high frequency

wind waves all around the bay once again from both the observational and model results. Even

though the data were not collected to study surface waves, results gathered from the model

studies verified that the observational data have a revealing pattern of the surface waves.

The reasons behind the attenuation of the swell waves have found to be:

Combined effect of bottom friction, depth-induced breaking and whitecapping,

Diffraction,

Refraction and,

Wave blocking.

After observing the differences between the refraction eliminated case and the rectangular bay

case, it has been seen that the geometry of the bay was reason for swell waves not to reach bay

mouth. Waves were blocked by the land especially beyond 20 km into the bay. According to the

calculations based on energy, 84% of the swell waves were blocked by the land before reaching

the head. The contribution of refraction was 14%. Bottom friction, depth induced wave

breaking and whitecapping did not seem to have a significant effect on swell attenuation. The

combined contribution of them was found to be around 1% to the attenuation. Diffraction' s

contribution was also found to be less than 1%.










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Long, C.E., Oltman-Shay, J.M. (1991): Directional characteristics of waves in shallow water,
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BIOGRAPHICAL SKETCH

The author was born in Ankara, Turkey on January 16th 1984. She lived in her hometown

Ankara for most of her life. She completed her primary, middle and high school education at

Buyuk High School, Ankara between September 1990 and June 2001. Then she was accepted to

the Civil Engineering program of Middle East Technical University, Ankara, in September 2001.

During her undergraduate education she developed a special interest in Coastal Engineering after

taking several courses on this area and she decided to seek a Master' s degree on Coastal

Engineering. After her graduation from collage in June 2005, she moved to Gainesville/Florida

to obtain her Master' s of Science degree in Coastal and Oceanographic Engineering from

University of Florida.