Indian Journal of Geo-Marine Sciences Vol. 39(4), December 2010, pp. 509-515

Wave refraction and energy patterns in the vicinity of Gangavaram, east coast of

K. V. S. R. Prasad, S. V. V. Arun Kumar*, Ch. Venkata Ramu & K. V. K. R. K. Patnaik Department of Meteorology and Oceanography, , – 530003, India *[E-mail: [email protected]]

Received 20 August 2010; revised 21 December 2010

Wave energy distribution along Gangavaram, east coast of India has been carried out for the predominant waves representing southwest monsoon (June-September), northeast monsoon (October-February) and storm period (March-May 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 south-south-east 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 in the south (Fig. 1). It is one of the deepest natural Wave refraction phenomenon is an important ports in India with a depth of about 20 m. The process responsible for effecting changes in coastal stations are identified on the location map showing configuration. Along the east coast of India, wave S1 to S13 on the southern side of the port and N1 to refraction studies were conducted using numerical 1,2,3 N9 towards north of the port. and traditional methods 4,5 . In the north coastal sector Climate in this region is mainly controlled by the of , these studies are very meager. Indian monsoons. The swell waves are having periods Visakhapatnam, the city of destiny consisting of two 5–10s 6,7 approaching from SSE and E directions ports: one near Dolphin’s nose and the other is newly during southwest monsoon and northeast monsoon constructed at a distance of just respectively. During storm conditions (considering 15 km southwards. These ports require frequent before and after storms also), the wave periods of 8- monitoring of wave conditions, littoral transport and 10s are predominant and sometimes 12-18s 8 are also bathymetry changes in order to maintain the ports and observed in both the seasons. Though the lower facilitate navigation. The present study deals with periods are dominant the higher periods are the ones wave refraction and distribution of nearshore wave which are important as far the energy distribution is energy patterns in the neighborhood of Gangavaram. concerned 3. The sea is rough during June to Gangavaram is located in the industrial nerve September with wave heights ranging from 1 to 3 m, center of north coastal Andhra Pradesh (latitude 17° and wave heights, of the order of 0.5 to 1 m prevail 37' N and longitude 83° 14' E). The coast here forms a during October to December, except during the bay between hill at north and Mukkoma hill at cyclone periods. south, and comprises of promontories, pocket beaches as well as open sandy beaches are peculiar for coastal Materials and Methods studies. A creek in between these two hills forms Based on wave atlas prepared for the Indian coast Balacheruvu lagoon, where the natural port of and past studies 5,7 , the predominant deep water wave Gangavaram has been developed mainly to cater to directions E and SSE, with periods 8 and 10 s the needs of the adjoining Visakhapatnam steel plant representing southwest (June-September) and north- 510 INDIAN J. MAR. SCI., VOL. 39 NO. 4, DECEMBER 2010

Fig. 1—Location map and study area. east monsoon (October-January) respectively are 3. Waves have small amplitude, constant period considered. In the , the frequency of and long crest 4 storms is more during March-May and October with 4. The speed of a wave with a given period at any wave periods 14s. Naval Hydrographic Charts 3002 location depends only on the depth of water at and 3035 were considered for extracting digital that location bathymetry using Arc Map software. Numerical 5. Changes in bottom topography are gradual refraction procedure is adapted from Skovgaard et al .9 6. Effects of current and winds are considerably and Mahadevan 3. Similar numerical refraction studies 1,2,3,10,11 negligible. were previously carried by many researchers for the Indian coast. In this study, we computed the Model details and computation of wave refraction nearshore wave energy and breaker conditions in The wave refraction pattern for the given area can addition to refraction and shoaling coefficients. be computed based on wave orthogonals and the

Assumptions of model 1 refraction coefficients, Kt = , which can be The computation of wave ray pattern is based on β linear small amplitude wave theory applied for obtained by solving the set of differential equations shallow waters. Accordingly the wave speed depends on the depth of the water in which it propagates. This d 2β dβ + p(s) + q(s)β = 0 model computes wave speed at every grid point under ds 2 ds the following assumptions:

1. Wave energy transmitted between adjacent 1 where, p(s) = − (cos θCx + sin θC y ) and orthogonal remains constant. This supposes C

that the lateral dispersion of energy along the 1 wave front, reflection of energy from sloping q(s) = (sin 2 θC − sin 2θC + cos 2 θC ) C xx xy yy bottom, and the loss of energy by friction and other processes are negligible. In order to solve these equations Runga-Kutta-Gill 2. The direction of wave advance is integration procedures are used 3. The procedure for perpendicular to the wave crest. wave refraction input details are explained in PRASAD et al. : WAVE REFRACTION AND ENERGY PATTERN 511

Appendix-I. The numerical computation requires the deep water wave direction. These conditions along water depths Hij at each grid point for computation of the x-axis form the initial conditions for the wave speed Cij . Other input data needed are the deep differential equations. water wave characteristics such as the wave period ( T Termination of model and extraction of breaker parameters in seconds), wave direction ( αο in degrees) and height The model computes the wave speed, wave angle (ho in meters). Therefore Cij can be calculated using the formula (with respect to x-axis), refraction coefficient ( Kr ), shoaling coefficient ( Ks ) and height ( hij ) at every grid   point and terminates under one/all of the following gT  2πH ij  Cij = tanh   conditions: 2π  Cij T  (a) Wave steepness hi j / L greater than 1/7 The model computes the wave speed and wave (b) Breaking depth db equals 1.28 hb height ( hij = ho K r K s ) by an iterative procedure at all (c) Wave ray reaches zero depth or any negative grid points, starting from the deep water of the model depth value (denotes land). Whenever breaking domain; the deep water wave speed provides the depth is reached, the model automatically initial approximation for the iterative procedure. For extracts the near shore wave height (breaker computing the wave speed at subsequent grid point height hb), breaker angle ( αb), shoaling and considered, the calculated at the previous points coefficient ( Ks), refraction coefficient ( Kr) and serves as the initial approximation. For depths less computes the near shore breaker energy using than L/2, where L is the deep water wave length, the 1 2 the formula, Eb = ρgh b . wave speed was computed from Cij = gH ij , 8 whenever Hij is less than 0.1 m; Cij was assumed to be zero. It is necessary to calculate the partial derivatives Results and Discussion of the wave speed with respect to x and y grid points. Wave refraction and Energy distribution With grid spacing as the unit of measurement for Southwest monsoon period – The refracted wave length in the horizontal plane, the finite difference orthogonals for the SSE direction and for the periods forms of the differential coefficients are 8 and 10s are shown in Fig. 2. For 8s wave period, convergence is observed near the south breakwater  C − C     C − C   ∂C   i+ ,1 j i− ,1 j  ∂C  i, j+1 i, j−1  and further southwards in the Appikonda beach at   =  ,  =    ∂x   2   ∂y   2  station S4 (Fig. 2a) with breaker heights 1.0-1.5 m  ∂ 2C   ∂ 2C  (Fig. 3a) and nearshore breaker energy is about     3 2   = Ci+ ,1 j − 2Ci, j + Ci− ,1 j ,  3.675 × 10 J/m (Table. 1). Waves of 10s period  ∂x2   ∂y 2  = C − 2C + C show more convergence of energy along the coast i, j+1 i, j i, j−1 (Fig. 2b) than that of 8s period with highest wave  2   C − C − C + C   ∂ C   i− ,1 j+1 i− ,1 j+1 i+ ,1 j−1 i− ,1 j−1  3 2   =   energy of 4.485 × 10 J/m at station S4. But, here the  ∂x∂y   4  convergence is just shifted southward (from S3 to S4). In the north of the port, divergence is observed Initial conditions with breaker heights 0.5-1.0m (Fig. 3a&b) having The integration of the differential equations is energies ranging between 1.482 × 10 3 J/m 2 (at station started offshore in the deep water where the wave N5) to 4.456 × 10 3 J/m 2 (at station N2). The shoaling rays are parallel, and proceeds towards the shore. The and refraction coefficients vary along this coast integration step size is expressed as a fraction of the ranging between 1.0-1.25 and 0.5-1.5, respectively. spatial grid spacing, the unit of measurement for The waves in the northern region are breaking at lengths in horizontal plane. As the x-axis of the deeper depths than usual due to the presence of rocky coordinated system is in deep water, the origin for the headlands and promontories of Yarada hills. During wave rays may be selected at equal intervals along the this season, most of the wave energy is concentrated x-axis. Where the refraction coefficient is 1, i.e., β = in the southern portion of the port and the 1, and its derivative is zero θ will be equal to the south breakwater is likely to be in the region of 512 INDIAN J. MAR. SCI., VOL. 39 NO. 4, DECEMBER 2010

Fig. 2—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.

3 2 Table 1—Near shore wave energy Eb (× 10 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 1.207 - 1.292 - 6.870 - S6 3.294 - 3.417 - 17.328 - S5 2.411 1.622 3.141 1.328 13.762 4.551 S4 2.407 3.675 2.474 4.485 8.064 11.908 S3 1.892 1.343 2.186 1.236 7.988 4.223 S2 1.534 2.460 1.616 4.022 5.713 15.804 S1 3.117 1.537 3.666 1.548 12.361 6.380

N1 1.819 1.694 1.647 1.537 5.570 3.632 N2 1.229 3.109 2.094 4.456 8.045 17.854 N3 1.537 3.253 1.732 2.484 9.000 8.405 N4 1.214 2.701 1.697 3.008 5.643 18.025 N5 - 1.504 - 1.482 - 4.922 N6 - 1.548 - 1.545 - 5.406

PRASAD et al. : WAVE REFRACTION AND ENERGY PATTERN 513

convergence. Because of the steep foreshore in the port (station S1) where rocky promontories exist and south the breaking waves may be plunging to surging further southwards in the Appikonda beach (station type. Due to the presence of the shoals in the north S6) with breaker heights 0.8-1.2m and wave energies and premature breaking, the waves seem to be less 3.117 × 10 3 J/m 2 and 3.294 × 10 3 J/m 2 respectively intense but due to rocky headlands all around, not except at rocky outcrops it is around 1.5 m (Fig 5a). safe for swimming. Recent news papers reported The wave convergence has shifted from the port many deaths at the headland of Yarada hill (stations break water during south-west monsoon to the station N3-N5) not due to rip currents but only due to sharp S1 during the season. At Appikonda beach secondary rocky bed. wave convergence is observed. Waves of 10s period Northeast monsoon period – Wave orthogonals show more convergence of energy along the coast approaching the coast from E direction and for the than that of 8s period as in case of southwest periods 8 and 10s are shown in Fig. 4. Waves of 8s monsoon. In the north of the port, divergence is period show convergence near the south side of the observed with breaker heights 0.5-0.8 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 2010

with energies 1.647 × 10 3 J/m 2 (at station N1) and in Fig. 6 (a & b). Wave orthogonals are converging 2.094 × 10 3 J/m 2 (at station N2). During this season, a near the south of port (station S1) and very far consistent convergence is also observed at the tip of southwards in Appikonda beach (station S6) for E the south breakwater. The intensity of wave waves and for SSE waves the convergence pattern is convergence and wave energy is reduced when shifted in the areas where there is divergence for E compared with that of south-west monsoon season. waves. For SSE waves, intense convergence patterns Storm period – The occurrence of are observed at stations S4, S2 and south breakwater. storms/cyclones is higher during pre monsoon During these conditions, breaker heights are observed (March-May) and post monsoon (October). to be reaching 3-4m (Fig. 7). In the northern portion, Vulnerability of the coast depends on the extent of waves are converging slightly at station N5 and the wave effect during storm periods 4. So, wave remaining is unaffected. In the south for storms refraction is also considered for 14s i.e., longer wave approaching from east, wave energies are very higher periods with 2 m deep water wave height for E (pre of the order 17.328 × 10 3 J/m 2 at station S6 and it monsoon) and SSE (post monsoon) waves and shown reduces to 5.713 × 10 3 J/m 2 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 in identifying vulnerable zones during storm and normal approach wave convergence is slight with higher conditions along Visakhapatnam coast, India, Natural Hazards , 49(2)(2009) 347 – 360, doi :10.1007/s11069-008- value at station N3 and N4. Whereas for waves 9297-4. approaching from south-south-east direction, the 5 Reddy, B.S.R., Venkata reddy, G. & Durga Prasad, N., Wave energies are surprisingly lower of 4.551 × 10 3 J/m 2 conditions & wave-induced longshore currents in the at station S5 and also observed that the convergence nearshore zone off Krishnapatnam, Indian J. Mar. Sci., 8(1979) 61-67. pattern is shifted towards north during this condition. 6 Chandramohan, P., Narasimha Rao, T.V., Panakala Rao, D. For stations N1 to N4 wave divergence is clearly & Prabhakara Rao, B., Studies on nearshore processes at observed as in case of seasonal waves (8s and 10s). yarada beach (South of Visakhapatnam harbour), east coast of India, Indian J. Mar. Sci., 13(1984) 164–167. Conclusions 7 Chandramohan P., Sanil Kumar, V. & Nayak, B.U., Wave During all seasons, higher wave energy pattern is statistics around the Indian Coast based on ship observed data, Indian J. Mar. Sci., 20(1991) 87–92. observed in the region to the south of the port but 8 Sanil Kumar, V., Ashok kumar, K. & Raju, N.S.N., Wave towards north complex wave conditions exist due to characteristics off Visakhapatnam coast during a cyclone, rocky headlands and promontories and as a result Curr. Sci., 86(11)(2004) 1524-1529. wave breaking transpires at deeper depths. Low wave 9 Skovgaard, O., Jonsson, I.G. & Bertelsen, J.A., Computation conditions are observed very near to north breakwater of wave heights due to refraction and friction, J. Waterways, Harbour Coastal Eng. Div. ASCE , 1(1975) 15-32. during all the seasons, even during storms. This may 10 Chandramohan, P., Sanil Kumar, V. & Nayak, B.U., Coastal be attributed to the presence of shoals in the vicinity. processes along the shorefront of Chilika lake, east coast of During storm conditions wave energies amplifies India, Indian J. Mar. Sci., 22(1993) 268–272. along the coast but for E waves it is much higher than 11 Sajeev, R., Chandramohan, P. & Sanil Kumar, V., Wave refraction and prediction of breaker parameters along the that of SSE waves on either side of the port South Kerala coast, India, Indian J. Mar. Sci., 26(1997) 128-134. breakwater is under the region of convergence during southwest monsoon and storms approaching in south- Appendix-I south-east direction. Numerical wave refraction The data input (Input.dat) required to trace the studies facilitate the coastal engineers and scientists orthogonals and to calculate the refraction, shoaling to understand the coastal processes and this model coefficients are: can be successfully adapted to any type of coast. 1. Total number of grid point along the x-axis: Acknowledgements NX

Authors are grateful to Prof. B. S. R. Reddy, for 2. Total number of grid point along the y-axis: his constructive suggestions during the progress of NY this work and acknowledges Dr. B. R. Subramaniam, 3. Whether depths at grid points printed (1) or Director, and Dr. V. Ranga Rao, Scientist, ICMAM not: PRNT=1 or 0 (default 1)

PD for constant encouragement and collaboration. 4. Number of orthogonal to be traced: NSET

Author (S. V. V. Arun Kumar) sincerely 5. Origin of the domain: X1, Y1 acknowledges C.S.I.R, New Delhi for providing 6. Orthogonal spacing: SPAC research fellowship. 7. Maximum number of possible steps involved in integration: MAX References 8. Integration step size: ISTEP 1 Angusamy, N., Udayaganesan, P. & Victor Rajamanickam, 9. Deep water wave period: T (in seconds) G., Wave refraction pattern and its role in the redistribution 10. Deep water wave direction with respect to x- of sediment along southern coast of Tamilnadu, India, Indian J. Mar. Sci., 27(1998) 173-178. axis of the model domain: THE (in degrees) 2 Chandramohan, P., Longshore sediment transport model 11. Deep water wave height: H (in meters) with particular reference to Indian coast , Ph.D. thesis, IIT Madras, India, 1988, pp. 210. Input.dat 3 Mahadevan R, Numerical calculation of wave refraction , 36 36 1 (National Institute of Oceanography, Goa, India, Technical 140 0 0 0.25 Report No. 2/83) 1983, pp. 28. 4 Prasad, K.V.S.R., Arun Kumar, S.V.V., Venkata, Ramu, Ch. 6000 0.05 & Sreenivas, P., Significance of nearshore wave parameters 8 80 1.0