Available online at www.sciencedirect.com ScienceDirect Aquatic Procedia 4 ( 2015 ) 41 – 48 INTERNATIONAL CONFERENCE ON WATER RESOURCES, COASTAL AND OCEAN ENGINEERING (ICWRCOE 2015) Tidal Hydrodynamics along Gulf of Khambhat, West Coast of India Sathish Kumar Sa, Balaji Rb* a Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India b Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India Abstract In coastal hydrodynamics, tides play a major role and it is important to understand the complexity of their characteristics along the difficult coastal areas like creeks, estuaries, bays and gulfs for any kind of engineering activities like harbor, jetty, dams and protection measures. In this study, six tidal constituents (K1, M2, N2, O1, P1 and S2) variations along the Gulf of Khambhat, west coast of India were studied with the spatially varied friction coefficient. A two-dimensional finite element-based numerical model (Telemac-2D) was developed and zones of different friction coefficients were identified by comparing numerically estimated levels and currents with that of measured and reported by earlier studies. Based on the comparisons, the gulf was divided into five zones of different bottom friction values. The numerical model was used to predict the tidal constituent’s propagation along the gulf with the spatially varied bottom friction values and the amplitude and currents were analysed along the gulf. From the results, it was observed that the M2 (semi-diurnal) and K1 (diurnal) constituents influence the hydrodynamics of the gulf of Khmabhat significantly, compared to the other constituents. Further, a composite tide, inclusive of all six tidal constituents was applied to the offshore boundary of the numerical model and the tidal levels and currents were analysed along the gulf locations. It was observed that the combined effect of the constituents further increase the tidal amplitude up to 10m and the velocity up to 4ms-1. The validation of the numerical model showed good agreement. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015. Peer-review under responsibility of organizing committee of ICWRCOE 2015 Keywords: Tidal hydrodynamics; Tidal constituents; Telemac-2D; Gulf of Khambhat; Friction coefficient * Corresponding author. Tel.: +0-22-2576-7321; fax: +0-22-2576-7302. E-mail address: [email protected] 2214-241X © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015 doi: 10.1016/j.aqpro.2015.02.007 42 S. Sathish Kumar and R. Balaji / Aquatic Procedia 4 ( 2015 ) 41 – 48 1. Introduction It is essential, for engineers and scientists, to understand the tidal hydrodynamics of particular coastal features like estuaries, gulfs and lagoons for any kind of coastal developments (harbors, ports, protection measures). Tide is composed of longest ocean waves which usually rises and falls every half day (semi-diurnal) or a day (diurnal). The change of water level due to tidal currents occurs everywhere in the ocean. However, the change is the most significant in the coastal zone due to the shallower water depth in the coastal region. To describe the strength of the tide, the difference in water elevation between high tide and low tide is called tidal range. Gulf of Khambhat is an inverted funnel shaped indentation on the west coast of India and spread over several hundred square kilometres, is one of the dynamic natural basins and having high tidal range (Siddiquie et al., 1981; Vora et al., 1980). The entire gulf is relatively shallow, compared to Arabian Sea, with the maximum water depth of about 30m. Tidal phase speed, along-channel amplitude growth, and tidal harmonics in strongly convergent channels are all linked by morphodynamics of that particular basin (Friedrichs and Aubrey, 1994). Complex geography of the gulf amplifies the tidal range to about 10m and tidal currents are about 3ms-1 (Giardino et al., 2014; Kumar and Kumar, 2010; Kumar et al., 2006). In geography, bed friction plays a vital role in tidal amplification. Unnikrishan et al., (1999) suggested that use of appropriate bottom friction coefficient will give better prediction. In this present study, study area is divided into five zones with appropriate friction coefficients based on the sensitivity analysis. Various data, measured during different period of time, are collected and systematically used to calibrate the numerical model. The calibrated model is then used to map the contours of amplitudes of selected tidal constituents (K1, M2, N2, O1, P1 and S2). 2. Numerical Model 2.1. Model Description A finite element based depth averaged numerical model has been developed to study the tidal hydrodynamics, using Telemac – 2D numerical scheme (Hervouet, 2007) which is capable of simulating free-surface flows in the two dimensions of horizontal space and solves the Saint-Venant equations. Basically, the Telemac-2D module solves the following averaged form of hydrodynamic continuous and momentum equations: wwhhUhV() w () 0 (1) wwtx wx ww()hU ( hUU ) w ( hUV ) wwwww Z§· U §·U gh¨¸ hveex ¨¸hv hF (2) wwtx w y wwwww xxxyy©¹©¹ ww()hV ( hUV ) w ( hVV ) wwwww Z§· V §·V gh¨¸ hveey ¨¸ hv hF (3) wwtx w y wwwww yxxyy©¹©¹ 2.2. Applied Forces in Momentum Equations 2.2.1. Bottom Friction Bottom friction, one of the applied forces, offers resistance to momentum of flow. In case of tidal propagation, the bottom friction in association with geometry and bathymetry, dictates the amplification of levels and magnitude of currents at any place of interest. The formula for friction force at the bottom, to be added to the momentum equation in the non-conservative form, takes as; S. Sathish Kumar and R. Balaji / Aquatic Procedia 4 ( 2015 ) 41 – 48 43 1 g 22 FUx 2 UV (4) CosD hC fr 1 g 22 FVy 2 UV (5) CosD hC fr 1/2 -1 The dimensionless friction parameter (Cfr) can be parameterised either in terms of Chezy (C, in m s ), Manning 1/3 -1 (m, in m s ), Strickler (S) or in Nikuradse (Ks,in mm) friction coefficients. Chezy’s friction coefficient is used for this study, which is applied by the following equation 2g C (6) fr C 2 2.2.2. Coriolis Force As the numerical model domain covers the entire gulf of large area, the effect of Coriolis force due to earth’s rotation on the momentum equation is also considered in this study. The following equations, defining Coriolis force along x and y directions are considered as source terms in the momentum equation: FVx 2sin()ZO (7) FUy 2sin()ZO (8) 2.3. Model Setup A relatively large model domain, covering entire Gulf of Khambhat and part of Arabian Sea, is considered for the numerical model with a size of about 650x750kms (16°N 68°E to 22°N 74°E) as shown in Fig. 1(a). The entire area is discretized into triangular grids, with a largest size of 50km along the offshore boundary and smallest size of 2km near the coastline. Finite element mesh of the area of study along with the bathymetry is shown in Fig. 1(b). The seabed contours for the model domain are extracted from various admiralty charts and the offshore boundary is forced with tidal constituents, obtained from global tidal models (Haigh, et al 2011). Fig. 1 (a) Study area and (b) bathymetry – Gulf of Khambhat 44 S. Sathish Kumar and R. Balaji / Aquatic Procedia 4 ( 2015 ) 41 – 48 2.4. Sensitivity Analysis Sensitivity analysis was carried out (Fernandes et al., 2001; Liu et al., 2009) to test the sensitivity to variations in bottom friction parameters in the numerical model (Telemac – 2D). To investigate the model sensitivity to different laws of bottom friction and the different values of friction coefficient were carried out by applying Chezy’s, Manning’s and Strickler’s laws of bottom friction. The effect on tidal currents for various laws of bottom friction and different friction coefficient values at Bombay High location is illustrated in Fig. 2. It is clear that the magnitude of the tidal current is also controlled by magnitude of the bottom friction coefficients. Fig. 2 Estimated tidal current at Bombay High (a) Chezy, (b) Manning, (c) Strickler laws of bottom friction and (A) typical scatter plot 3. Calibration and Validation Initially available data from various resources (Diwan et al., 1991; Giardino et al., 2014; Naidu et al., 2013; Sinha et al., 2010; Swamy et al., 1982; Unnikrishnan, 2010; Unnikrishnan et al., 1999; Vora et al., 1980) are collected all along the gulf, and the locations are shown in Fig. 1(a). Part of the above mentioned data used for calibration, which covers the east and west coast of the gulf and rest of the collected data used for validation of the developed numerical model. Model domain is divided into five zones which are based on the bathymetry of the gulf numbered from offshore to nearshore. Based on the sensitivity analysis, Chezy’s bottom friction coefficient for each zone is calibrated using the available data. Fig. 3(a) shows the different zones and corresponding friction coefficient as a function of water depth. It is observed that the friction values are increasing with decrease in water depths from offshore region, except near head of gulf, where a relatively low friction coefficient yield a fair agreement between numerical and available data. The relationship between maximum water depth of each zone and friction coefficients appears to be following a trend, as shown in the Fig.