Wave Transformation in the Surf- Zone of Pondicherry Coast

Wave Transformation in the Surf- Zone of Pondicherry Coast

Dr. G. Vijayakumar *, Dr. D. Govindarajulu **, Dr. T. Sundararajan**

*Associate Professor, **Professor Department of Civil Engineering,

Pondicherry Engineering College, Pondicherry.

Abstract

Transformation of near shore waves at the surf zone attribute to the morphological change of a coast. For the study, the Veerampattinam beach located at the Pondicherry region was selected. The beach is straight and extend to about three Km. The breaking wave height was determined from the available deep sea wave data acquired from the wave float gauge designed by the department of Civil Engineering, Pondicherry Engineering College, Pondicherry (Vijayakumar, G., Pandurangan, K., and Govindarajulu, D.,(2004). The type of transformation of waves at the surf zone was determined by analytical approach using Matlab software. From the model developed based on the observed wave climate data and bathymetry of the area for a period of one year(June 2008 May 2009), it was found that , the predominant type of breaking was plunging which has occurred from the Month of October to January which is mainly responsible for sediment transport and modification of beach profile. From the month of June to September the predominant type of breaking was collapsing and surging which are responsible for steepening of beach ( Aagaard,T., Robin,D-A., Greenwood,B., Nielson,J., (2004),.

Index Terms: Beach Morphology, spilling, plunging, surging, collapsing, wave float gauge

1. Introduction

   Wave approaching the coast increase in steepness (H/L) as the water depth decreases (Andrew, C.J.F., 1999). However, there is a physical limit to the steepness of the waves and when this physical limit is exceeded, the wave becomes unstable and breaks, dissipating energy and inducing near-shore currents and an increase in mean water level (Bayram, A., Larson, M., 2000). Waves break in a water depth approximately equal to the wave height. The surf Zone is the region extending from the seaward boundary of wave breaking to the limit of wave up rush. Within the surf Zone, wave breaking is the dominant hydrodynamic process. The surf zone is the most dynamic coastal region with sediment transport and bathymetry change driven by breaking waves and near shore currents (Chen Y- Y., Yang, B-D., Tang, L -W., Ou, S _H.,

   Hsu, J.R- C., 2004). Surf zone wave transformation study is an essential tool to estimate potential storm damage, shoreline evolution and cross shore beach profile change, and in the design coastal strucutures (jetties, groins, seawalls ) and

   beach fills (Gadre, M.R., Kantkar, C.N., 1989).

   1.1 Breaker Types

   As a wave approaches a beach, its length

   (L) decreases and its height (H) may increase, causing the wave steepness (H/L) to increase. Wave breaks as they reach a limiting steepness, which is a function of the relative depth (d/L) and the beach slope (tan) (Bayram, A., Larson, M., 2000). Wave breaking parameters, both qualitatively and quantitative, are needed in a wide variety of coastal engineering applications. Breaker type refers to the form of the wave at breaking. Wave breaking is classified under four types as: spilling, plunging ,collapsing and surging (Galvin 1968). The breaker type is a function of the beach slope (tan = m) and the wave steepness (H/L). These may be combined into a ratio, usually called the surf similarity parameter, as Eqn.(1):

   b = m / (Hb / Lo)0.5 —(1)

   1. Spilling breakers

      Spilling breakers, Battjes (1974) occur when b < 0.4. This type of breaking waves occur when the approaching nearshore consists of a flat beach for steep waves or both. Therefore when sea breaks on a flat sandy beach, the breakers are predominantly of spilling type. Several

      wave crests may be breaking simultaneously, giving the appearance of several rows of breaking waves throughout the breaking zone. Such beaches are often called as dissipative beaches (Battjes 1974).

   2. Plunging breakers

      Plunging breakers occurs on steeper beaches and /or for flatter waves, when

      0.4. < b < 2.0. In this case, the wave crest runs ahead of the main body of the wave and plunges forward violently. This type of breaking of waves tend to roll and break thereby creating a slurry in the breaking area and makes the sediment to be in suspension and move in lateral direction depending on the cross – shore current. Hence, this type of breaking waves are more responsible of sediment movement ( Battjes 1974).

   3. Collapsing

      Collapsing type of breaking occurs when b > 2.0. These waves are characterized by a wave front that more or less explodes forward , may be found where swell breaks on steep beaches made up of coarse material ( Battjes 1974).

   4. Surging

   Surging breakers occur on very steep beaches. The waves simply surge up and down the beach and there is very little or no breaking. Beaches with surging and

   collapsing breakers are often called

   reflective beaches( Battjes 1974). A schematic view of different types of breakers is shown in Fig. 1.

   (Harrison and Wilson 1964, Dobson 1967, Noda et al. 1974). Refraction and shoaling analyses typically try to specify the wave

   height and direction along a ray.

   Beach is very Flat

   Beach is usually Flat

   Spilling

   Plunging

   Beach is usually Steep

   Beach is very Steep

   Collapsing

   Surging

   From the wave data acquired from the wave float installed near the pier of the Pondicherry port was collected for the above said period from which, the average values of wave height of each month (Hs), wave length (L), o (wave direction), significant wave period (Ts) constitute the input parameters for wave transformation

   Fig.1.Typess of Breaker

2. Methodology

   1. Breaking wave height

      1. Wave Ray Method

         The wave-propagation problem can often be readily visualized by construction of wave rays Fig.2. If a point on a wave crest is selected and a wave crest orthogonal is drawn, the path traced out by the orthogonal as the wave crest propagates onshore is called a ray. Hence, a group of wave rays map the path of travel of the wave crest. For simple bathymetry, a group of rays can be constructed by hand to show the wave transformation,

         studies. Eqn. (2 ), (3), (4), and (5) were used to obtain the wave parameters corresponding to deep water condition and then to obtain the transformed wave height at incipient wave breaking condition i.e, (Hb) (Bayram, A., Larson, M., 2000). This value of Hb will be subsequently used in the surf zone transformation studies (Bryant, E. (1979). Using a standard commercial package (MS Excel) the above computations were carried out and the output consists of, b and Hb for each month for the year 2009 Table.1 .

         Fig.2 Idealized plot of wave rays

         Hd at any depth can be related to deep water wave height Ho as:

         gT/2tanh(2d/L) gd/F

         where, gd/F an approximation for the wave celerity and

         Hd/H0 = n0C0/nC

         = 1/[2 n tanh(kd)] = Ks (2)

         F = G +

         and

         1

         1.0 + 0.6522G + 0.4622G2 + 0.0864G4 + 0.0675 G5

         G = 2 (d/Lo) = (2 /T)2 d/g

         Hd/H0 = n0 C0 b0/n C b

         = 1/ [2n tanh(kd)] b0/b = Ks. Kr

         where, Kr = b0/b, is called the refraction coefficient= (cos0/ cos)1/2

         = (1 sin20/1 sin2)1/4 ….(3)

         Where ,g = gravitational acceleration L/Lo

         = shallow and deep water wave length d = depth of wave at breaking

         d can be taken approximately equal to Hb (breaking wave height)

         Sl. No.	Month	Hb(app)	b
         1	Jan	1.07	19.08
         2	Feb	0.80	18.25
         3	March	0.71	12.40
         4	April	0.79	14.08
         5	May	0.96	14.29
         6	June	0.97	15.47
         7	July	0.68	17.06
         8	August	0.76	18.06
         9	Sept	1.13	10.75
         10	Oct	1.04	12.66
         11	Nov	0.87	18.36
         12	Dec	1.00	21.31

         Sl. No.	Month	Hb(app)	b
         1	Jan	1.07	19.08
         2	Feb	0.80	18.25
         3	March	0.71	12.40
         4	April	0.79	14.08
         5	May	0.96	14.29
         6	June	0.97	15.47
         7	July	0.68	17.06
         8	August	0.76	18.06
         9	Sept	1.13	10.75
         10	Oct	1.04	12.66
         11	Nov	0.87	18.36
         12	Dec	1.00	21.31

         where,

         Ks&Kr = Shoaling and Refraction coefficient

         0 = wave angle at deep water.

         b/bo = Distance between adjacent wave rays, at breaking and deep

         C/Co = Wave celerity at shallow and deep

         n = Number of waves recorded

         Hd = Ho ( tanh kd(1 + (2 kd/ sinh kd)))0.5 (4)

         Where,

         H0 =deep water wave height (in m);

         Hd = wave height measured at depth d (in m);

         d = depth of wave measured (in m); k = wave number = 2 / L and

         L = wave length (in m) The wavelength is then given as

         L =T gd/F .(5)

         Table 1. Breaking wave height (Hb) and wave angle (b) year 2009

         2.2 Near shore transformation

         2.2.1 Analytical Model

         Near shore wave height obtained by the wave ray method, the deepwater wave length and the slope were used to evaluate the surf similarity parameter( b) using Eqn.(1), for each month for the observatory period(June 2008-May 2009) . Based on the value of b obtained, the type of wave breaking was determined. A separate program was developed for the above in Matlab (ver.7.0) which is listed in Appendix 1.

3. Results and Discussion

   The type of wave breaking for each month of the year 2009 is given in Tables 2. It can be seen that during October January (N E monsoon) the predominant type of breaking is plunging, thus contributing to the sediment movement, in this part of the coast. During S W monsoon (June- September) the predominant type of breaking is surging and collapsing which is responsible for steepening of the beach.

4. Conclusion

Result from near shore transformation studies show that the numerical solution gives better results and can closely represent the physical phenomenon of waves in near-shore. The type of breaking has been identified based on the surf

similarity parameter and its influence on the coastal process has been identified.

Table2. Types of near shore wave breaking year 2009

Appendix I

Mat lab programme for determining the type of wave breaking

d = input(enter depth at breaker zone:n) ratio _ of _ depth _ to _ wave _length = (d/wave _length)

ratio _ of _wave _heights = input(enter the ratio of wave heights corresponding to that of d/lo:n)

significant _ wave _ height _ in _ breaker

_ zone = (significant _ wave height _ in _ metres)*( ratio _ of _ wave _ heights) slope(m) = 0.03

c = sqrt(significant _ wave _ height _ in _ breaker _ zone/ wave _ length);

surf _ similarity _ parameter = m/c

if (surf _ similarity _ parameter < 0.4) fprintf(Type _ of _ breaker _ is _ spilling\n)

elseif(surf _ similarity _ parameter > 0.4 ) & ( surf _ similarity _ parameter < 2.0) fprintf(Type _ of _ breaker _ plunging

\n)

elseif(surf _ similarity _ parameter > 2.0) fprintif(Type _ of _ breaker _ collapsing \ n)

5 Reference:

1. Andrew, C.J.F., (1999), Bibliographic review of nearshore wave models, DSTO Aeronautical and Maritime Research Laboratory, Report No. AR- 011- 030, 65 pp

2. Aagaard,T.,Robin,D-A., Greenwood,B., Nielson,J., (2004),. Sand Bed Oscillations and Suspended Sediment Flux during an Accretionary Phase of the Foreshore Cycle, Danish Journal of Geography 104(1):15-30.

3. Bayram, A., Larson, M., (2000), Wave transformation in the nearshore zone : comparison between a Boussinesq model and field data, Coastal Engineering, 39: 149 171.

4. Battjes, J.A.,(1974),Surf Similarity Parameter Proc. of 14th Intl. Conf. on Coastal Engineering, Copenhagen, 69-85

5. Bryant , E. (1979), Comparison of computed and observed breaker wave heights, Coastal Engineering, 3(1): 39 50.

6. Chen Y-Y., Yang, B-D., Tang, L -W., Ou, S _H., Hsu, J.R- C., (2004),

   Transformation of progressive waves propagating obliquely on gentle slope, ASCE Jl. of waterway, Port, Coastal and Ocean Engg., 130(4): 162 169.

7. Dobson, R.S. 1967. Some Applications of a Digital Computer to Hydraulic Engineering Problems, Technical Report No. 80, Department of Civil Engineering, Stanford University, Stanford, CA.

8. Gadre, M.R., Kantkar, C.N., (1989),

   Wave transformation in MIRYA bay , Ratnagri, 3rd Indian Natl. Conf. on Dock and Harbour Engineering , Dec 6-8, KREC, Suratkal, India , 85 92 (Vol I).

9. Galvin, C. J. (1968). Breaker type classifications of three laboratory beaches,Journal of Geophysical Research 73, 3651-3659.

10. Harrison, W., and Wilson, W. S. 1964. Development of a Method for Numerical Calculation of Wave Refraction, Technical Memorandum No. 6, Coastal Engineering Research Center,

    U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

11. Noda, E. K., et al. 1974. Nearshore Circulations Under Sea Breeze Conditions and Wave-Current Interactions in the Surf Zone, Technical Report No. 4, Tetra Tech, Inc., Pasadena, CA.

12. Vijayakumar, G., Pandurangan, K., and Govindarajulu, D.,(2004) A Simple low cost wave measurement system, 3rd Indian Natl. Conf. on Harbour & Ocean Engineering, NIO, Goa, Dec. 7-9, India , 777 784, (Vol II).