Indian Journal of GeoMarine Sciences Vol. 39(4), December 010, pp. 509515 Wave refraction and energy patterns in the vicinity of Gangavaram, east coast of India K. V. S. R. Prasad, S. V. V. Arun Kumar*, Ch. Venkata Ramu & K. V. K. R. K. Patnaik Department of Meteorology and Oceanography, Andhra University, Visakhapatnam 530003, India *[Email: arunocean@gmail.com] Received 0 August 010; revised 1 December 010 Wave energy distribution along Gangavaram, east coast of India has been carried out for the predominant waves representing southwest monsoon (JuneSeptember), northeast monsoon (OctoberFebruary) and storm period (MarchMay and October) using a wave refraction model. Model computes refraction coefficient, shoaling coefficient, breaker heights and breaker energies along the coast. During all seasons, higher wave energy pattern is observed in the region to the south of the port but towards north, complex wave conditions exist due to rocky headlands and promontories and as a result wave breaking transpires at deeper depths. Low wave energy conditions are observed very near to north breakwater during all the seasons and even during storms. During storm conditions wave energies amplify along the coast. South breakwater of the port is under the region of convergence during southwest monsoon and for the storms approaching in southsoutheast direction. Numerical wave refraction studies facilitate the coastal engineers and scientists to understand the coastal processes. [Keywords: Wave refraction, Refraction model, Nearshore, Gangavaram coast] Introduction Wave refraction phenomenon is an important process responsible for effecting changes in coastal configuration. Along the east coast of India, wave refraction studies were conducted using numerical 1,,3 and traditional methods 4,5. In the north coastal sector of Andhra Pradesh, these studies are very meager. Visakhapatnam, the city of destiny consisting of two ports: one near Dolphin s nose and the other is newly constructed Gangavaram port at a distance of just 15 km southwards. These ports require frequent monitoring of wave conditions, littoral transport and bathymetry changes in order to maintain the ports and facilitate navigation. The present study deals with wave refraction and distribution of nearshore wave energy patterns in the neighborhood of Gangavaram. Gangavaram is located in the industrial nerve center of north coastal Andhra Pradesh (latitude 17 37' N and longitude 83 14' E). The coast here forms a bay between Yarada hill at north and Mukkoma hill at south, and comprises of promontories, pocket beaches as well as open sandy beaches are peculiar for coastal studies. A creek in between these two hills forms Balacheruvu lagoon, where the natural port of Gangavaram has been developed mainly to cater to the needs of the adjoining Visakhapatnam steel plant in the south (Fig. 1). It is one of the deepest natural ports in India with a depth of about 0 m. The stations are identified on the location map showing S1 to S13 on the southern side of the port and N1 to N9 towards north of the port. Climate in this region is mainly controlled by the Indian monsoons. The swell waves are having periods 5 10s 6,7 approaching from SSE and E directions during southwest monsoon and northeast monsoon respectively. During storm conditions (considering before and after storms also), the wave periods of 8 10s are predominant and sometimes 118s 8 are also observed in both the seasons. Though the lower periods are dominant the higher periods are the ones which are important as far the energy distribution is concerned 3. The sea is rough during June to September with wave heights ranging from 1 to 3 m, and wave heights, of the order of 0.5 to 1 m prevail during October to December, except during the cyclone periods. Materials and Methods Based on wave atlas prepared for the Indian coast and past studies 5,7, the predominant deep water wave directions E and SSE, with periods 8 and 10 s representing southwest (JuneSeptember) and north
510 INDIAN J. MAR. SCI., VOL. 39 NO. 4, DECEMBER 010 Fig. 1 Location map and study area. east monsoon (OctoberJanuary) respectively are considered. In the Bay of Bengal, the frequency of storms is more during MarchMay and October 4 with wave periods 14s. Naval Hydrographic Charts 300 and 3035 were considered for extracting digital bathymetry using Arc Map software. Numerical refraction procedure is adapted from Skovgaard et al. 9 and Mahadevan 3. Similar numerical refraction studies were previously carried by many researchers 1,,3,10,11 for the Indian coast. In this study, we computed the nearshore wave energy and breaker conditions in addition to refraction and shoaling coefficients. Assumptions of model The computation of wave ray pattern is based on linear small amplitude wave theory applied for shallow waters. Accordingly the wave speed depends on the depth of the water in which it propagates. This model computes wave speed at every grid point under the following assumptions: 1. Wave energy transmitted between adjacent orthogonal remains constant. This supposes that the lateral dispersion of energy along the wave front, reflection of energy from sloping bottom, and the loss of energy by friction and other processes are negligible.. The direction of wave advance is perpendicular to the wave crest. 3. Waves have small amplitude, constant period and long crest 4. The speed of a wave with a given period at any location depends only on the depth of water at that location 5. Changes in bottom topography are gradual 6. Effects of current and winds are considerably negligible. Model details and computation of wave refraction The wave refraction pattern for the given area can be computed based on wave orthogonals and the 1 refraction coefficients, K t =, which can be β obtained by solving the set of differential equations d β dβ + p( s) + q( s) β = 0 ds ds 1 where, p( s) = (cosθ C x + sinθc y ) and C 1 q( s) = (sin θ Cxx sin θc xy + cos θc C In order to solve these equations RungaKuttaGill integration procedures are used 3. The procedure for wave refraction input details are explained in yy )
PRASAD et al.: WAVE REFRACTION AND ENERGY PATTERN 511 AppendixI. The numerical computation requires the water depths H ij at each grid point for computation of wave speed C ij. Other input data needed are the deep water wave characteristics such as the wave period (T in seconds), wave direction (α ο in degrees) and height (h o in meters). Therefore C ij can be calculated using the formula C ij gt πh = tanh π CijT ij The model computes the wave speed and wave height ( h = h K K ) by an iterative procedure at all ij o r s grid points, starting from the deep water of the model domain; the deep water wave speed provides the initial approximation for the iterative procedure. For computing the wave speed at subsequent grid point and considered, the calculated at the previous points serves as the initial approximation. For depths less than L/, where L is the deep water wave length, the wave speed was computed fromc ij = gh ij, whenever H ij is less than 0.1 m; C ij was assumed to be zero. It is necessary to calculate the partial derivatives of the wave speed with respect to x and y grid points. With grid spacing as the unit of measurement for length in the horizontal plane, the finite difference forms of the differential coefficients are C Ci+ 1, j Ci 1, j C Ci, 1 C =, = x y C C = + C +, i 1, j Ci, j Ci 1, j x y = Ci, 1 Ci, j + Ci, j 1 C Ci 1, 1 Ci 1, 1 Ci+ 1, j 1 + Ci 1, j = x y 4 i, j 1 Initial conditions The integration of the differential equations is started offshore in the deep water where the wave rays are parallel, and proceeds towards the shore. The integration step size is expressed as a fraction of the spatial grid spacing, the unit of measurement for lengths in horizontal plane. As the xaxis of the coordinated system is in deep water, the origin for the wave rays may be selected at equal intervals along the xaxis. Where the refraction coefficient is 1, i.e., β = 1, and its derivative is zero θ will be equal to the 1 deep water wave direction. These conditions along the xaxis form the initial conditions for the differential equations. Termination of model and extraction of breaker parameters The model computes the wave speed, wave angle (with respect to xaxis), refraction coefficient (Kr), shoaling coefficient (Ks) and height (h ij ) at every grid point and terminates under one/all of the following conditions: (a) Wave steepness h i j / L greater than 1/7 (b) Breaking depth d b equals 1.8 h b (c) Wave ray reaches zero depth or any negative depth value (denotes land). Whenever breaking depth is reached, the model automatically extracts the near shore wave height (breaker height h b ), breaker angle (α b ), shoaling coefficient (K s ), refraction coefficient (K r ) and computes the near shore breaker energy using 1 the formula, Eb = ρgh b. 8 Results and Discussion Wave refraction and Energy distribution Southwest monsoon period The refracted wave orthogonals for the SSE direction and for the periods 8 and 10s are shown in Fig.. For 8s wave period, convergence is observed near the south breakwater and further southwards in the Appikonda beach at station S4 (Fig. a) with breaker heights 1.01.5 m (Fig. 3a) and nearshore breaker energy is about 3.675 10 3 J/m (Table. 1). Waves of 10s period show more convergence of energy along the coast (Fig. b) than that of 8s period with highest wave energy of 4.485 10 3 J/m at station S4. But, here the convergence is just shifted southward (from S3 to S4). In the north of the port, divergence is observed with breaker heights 0.51.0m (Fig. 3a&b) having energies ranging between 1.48 10 3 J/m (at station N5) to 4.456 10 3 J/m (at station N). The shoaling and refraction coefficients vary along this coast ranging between 1.01.5 and 0.51.5, respectively. The waves in the northern region are breaking at deeper depths than usual due to the presence of rocky headlands and promontories of Yarada hills. During this season, most of the wave energy is concentrated in the southern portion of the port and the south breakwater is likely to be in the region of
51 INDIAN J. MAR. SCI., VOL. 39 NO. 4, DECEMBER 010 Fig. Wave refraction for SSE waves: (a) 8s period (b) 10s period. Fig. 3 Variation of breaker parameters for SSE waves: (a) 8s and (b) 10s. Table 1 Near shore wave energy E b ( 10 3 J/m ) for different wave conditions Station T = 8 sec T = 10 sec T = 14 sec ID E waves SSE waves E waves SSE waves E waves SSE waves S7 S6 S5 S4 S3 S S1 1.07 3.94.411.407 1.89 1.534 3.117 1.6 3.675 1.343.460 1.537 1.9 3.417 3.141.474.186 1.616 3.666 1.38 4.485 1.36 4.0 1.548 6.870 17.38 13.76 8.064 7.988 5.713 1.361 4.551 11.908 4.3 15.804 6.380 N1 N N3 N4 N5 N6 1.819 1.9 1.537 1.14 1.694 3.109 3.53.701 1.504 1.548 1.647.094 1.73 1.697 1.537 4.456.484 3.008 1.48 1.545 5.570 8.045 9.000 5.643 3.63 17.854 8.405 18.05 4.9 5.406
PRASAD et al.: WAVE REFRACTION AND ENERGY PATTERN 513 convergence. Because of the steep foreshore in the south the breaking waves may be plunging to surging type. Due to the presence of the shoals in the north and premature breaking, the waves seem to be less intense but due to rocky headlands all around, not safe for swimming. Recent news papers reported many deaths at the headland of Yarada hill (stations N3N5) not due to rip currents but only due to sharp rocky bed. Northeast monsoon period Wave orthogonals approaching the coast from E direction and for the periods 8 and 10s are shown in Fig. 4. Waves of 8s period show convergence near the south side of the port (station S1) where rocky promontories exist and further southwards in the Appikonda beach (station S6) with breaker heights 0.81.m and wave energies 3.117 10 3 J/m and 3.94 10 3 J/m respectively except at rocky outcrops it is around 1.5 m (Fig 5a). The wave convergence has shifted from the port break water during southwest monsoon to the station S1 during the season. At Appikonda beach secondary wave convergence is observed. Waves of 10s period show more convergence of energy along the coast than that of 8s period as in case of southwest monsoon. In the north of the port, divergence is observed with breaker heights 0.50.8 m (Fig. 5) and Fig. 4 Wave refraction for E waves: (a) 8s period (b) 10s period. Fig. 5 Variation of breaker parameters for E waves: (a) 8s and (b) 10s.
514 INDIAN J. MAR. SCI., VOL. 39 NO. 4, DECEMBER 010 with energies 1.647 10 3 J/m (at station N1) and.094 10 3 J/m (at station N). During this season, a consistent convergence is also observed at the tip of the south breakwater. The intensity of wave convergence and wave energy is reduced when compared with that of southwest monsoon season. Storm period The occurrence of storms/cyclones is higher during pre monsoon (MarchMay) and post monsoon (October). Vulnerability of the coast depends on the extent of wave effect during storm periods 4. So, wave refraction is also considered for 14s i.e., longer wave periods with m deep water wave height for E (pre monsoon) and SSE (post monsoon) waves and shown in Fig. 6 (a & b). Wave orthogonals are converging near the south of port (station S1) and very far southwards in Appikonda beach (station S6) for E waves and for SSE waves the convergence pattern is shifted in the areas where there is divergence for E waves. For SSE waves, intense convergence patterns are observed at stations S4, S and south breakwater. During these conditions, breaker heights are observed to be reaching 34m (Fig. 7). In the northern portion, waves are converging slightly at station N5 and the remaining is unaffected. In the south for storms approaching from east, wave energies are very higher of the order 17.38 10 3 J/m at station S6 and it reduces to 5.713 10 3 J/m at station S1 nearer to Fig. 6 Wave refraction for storm conditions of 14s period: (a) E waves (b) SSE waves. Fig. 7 Variation of breaker parameters for (a) E waves and (b) SSE waves during storms.
PRASAD et al.: WAVE REFRACTION AND ENERGY PATTERN 515 south breakwater. In the north, for the same wave approach wave convergence is slight with higher value at station N3 and N4. Whereas for waves approaching from southsoutheast direction, the energies are surprisingly lower of 4.551 10 3 J/m at station S5 and also observed that the convergence pattern is shifted towards north during this condition. For stations N1 to N4 wave divergence is clearly observed as in case of seasonal waves (8s and 10s). Conclusions During all seasons, higher wave energy pattern is observed in the region to the south of the port but towards north complex wave conditions exist due to rocky headlands and promontories and as a result wave breaking transpires at deeper depths. Low wave conditions are observed very near to north breakwater during all the seasons, even during storms. This may be attributed to the presence of shoals in the vicinity. During storm conditions wave energies amplifies along the coast but for E waves it is much higher than that of SSE waves on either side of the port South breakwater is under the region of convergence during southwest monsoon and storms approaching in southsoutheast direction. Numerical wave refraction studies facilitate the coastal engineers and scientists to understand the coastal processes and this model can be successfully adapted to any type of coast. Acknowledgements Authors are grateful to Prof. B. S. R. Reddy, for his constructive suggestions during the progress of this work and acknowledges Dr. B. R. Subramaniam, Director, and Dr. V. Ranga Rao, Scientist, ICMAM PD for constant encouragement and collaboration. Author (S. V. V. Arun Kumar) sincerely acknowledges C.S.I.R, New Delhi for providing research fellowship. References 1 Angusamy, N., Udayaganesan, P. & Victor Rajamanickam, G., Wave refraction pattern and its role in the redistribution of sediment along southern coast of Tamilnadu, India, Indian J. Mar. Sci., 7(1998) 173178. Chandramohan, P., Longshore sediment transport model with particular reference to Indian coast, Ph.D. thesis, IIT Madras, India, 1988, pp. 10. 3 Mahadevan R, Numerical calculation of wave refraction, (National Institute of Oceanography, Goa, India, Technical Report No. /83) 1983, pp. 8. 4 Prasad, K.V.S.R., Arun Kumar, S.V.V., Venkata, Ramu, Ch. & Sreenivas, P., Significance of nearshore wave parameters in identifying vulnerable zones during storm and normal conditions along Visakhapatnam coast, India, Natural Hazards, 49()(009) 347 360, doi :10.1007/s11069008 9974. 5 Reddy, B.S.R., Venkata reddy, G. & Durga Prasad, N., Wave conditions & waveinduced longshore currents in the nearshore zone off Krishnapatnam, Indian J. Mar. Sci., 8(1979) 6167. 6 Chandramohan, P., Narasimha Rao, T.V., Panakala Rao, D. & Prabhakara Rao, B., Studies on nearshore processes at yarada beach (South of Visakhapatnam harbour), east coast of India, Indian J. Mar. Sci., 13(1984) 164 167. 7 Chandramohan P., Sanil Kumar, V. & Nayak, B.U., Wave statistics around the Indian Coast based on ship observed data, Indian J. Mar. Sci., 0(1991) 87 9. 8 Sanil Kumar, V., Ashok kumar, K. & Raju, N.S.N., Wave characteristics off Visakhapatnam coast during a cyclone, Curr. Sci., 86(11)(004) 154159. 9 Skovgaard, O., Jonsson, I.G. & Bertelsen, J.A., Computation of wave heights due to refraction and friction, J. Waterways, Harbour Coastal Eng. Div. ASCE, 1(1975) 153. 10 Chandramohan, P., Sanil Kumar, V. & Nayak, B.U., Coastal processes along the shorefront of Chilika lake, east coast of India, Indian J. Mar. Sci., (1993) 68 7. 11 Sajeev, R., Chandramohan, P. & Sanil Kumar, V., Wave refraction and prediction of breaker parameters along the Kerala coast, India, Indian J. Mar. Sci., 6(1997) 18134. AppendixI The data input (Input.dat) required to trace the orthogonals and to calculate the refraction, shoaling coefficients are: 1. Total number of grid point along the xaxis: NX. Total number of grid point along the yaxis: NY 3. Whether depths at grid points printed (1) or not: PRNT=1 or 0 (default 1) 4. Number of orthogonal to be traced: NSET 5. Origin of the domain: X1, Y1 6. Orthogonal spacing: SPAC 7. Maximum number of possible steps involved in integration: MAX 8. Integration step size: ISTEP 9. Deep water wave period: T (in seconds) 10. Deep water wave direction with respect to x axis of the model domain: THE (in degrees) 11. Deep water wave height: H (in meters) Input.dat 36 36 1 140 0 0 0.5 6000 0.05 8 80 1.0