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 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 *[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 Andhra Pradesh, 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 Gangavaram port 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 Yarada 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 Bay of Bengal, 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).