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Tidal Modelling in the Gulf of Khambhat Based on a Numerical and Analytical Approach

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Tidal Modelling in the Gulf of Khambhat Based on a Numerical and Analytical Approach Indian Journal of Marine Sciences Vol. 43(7), July 2014, pp. Tidal modelling in the Gulf of Khambhat based on a numerical and analytical approach A. Giardino1*, E. Elias1, A. Arunakumar2& K. Karunakar2 1Deltares, Unit Marine and Coastal Systems, Department of Morphology and Sediment Dynamics, Rotterdamseweg 185, P.O. Box 177, 2600 MH Delft,The Netherlands 2National Institute of Ocean Technology,Pallikaranai, Chennai- 600 100, India *[Email: [email protected]] Received 22 August 2013; revised 22 October 2013 In this study, a two-dimensional numerical model of the Gulf has been implemented based on the Delft3D code to study the tidal propagation in the basin. Model has been calibrated and validated versus tidal measurements. Moreover, an analytical model for tidal propagation in converging estuary has been implemented based on the analytical work of Van Rijn (2011a). Two models show a good agreement, also with respect to observations. Moreover, the use of an analytical model with very low computational time, in support to a more sophisticated but computational time consuming numerical model, allows for an easy understanding of the different geometrical parameters (e.g. convergence length, water depth) and physical processes (e.g. damping due to bottom friction, tidal shoaling due to funnelling shape, tidal reflection) affecting the system and for an interpretation of the results of the more complex Delft3D numerical model. The effects of external changes on the physical system (e.g. impact of sea level rise) can also be easily accessed by means of a simple analytical model. [Keywords: Gulf of Khambhat, tides, Delft3D numerical model, analytical model, tidal amplification, sea level rise.] Introduction nature and interpretation of the main physical The prediction of tidal characteristics in gulfs processes. and estuaries is extremely important as tidal In this paper, the tidal dynamics in the Gulf of dynamics have a direct impact on the design of any Khambhat have been investigated using a engineering infrastructure built in these areas. numerical and an analytical approach, and validated Several economical activities (e.g. shipping, oil and using field data. The process-based numerical water extraction) as well as the flora and fauna can model allows for a detail description of the tidal be directly or indirectly influenced by the tidal dynamics in the gulf. Next to it, the use of a simple ranges and tidal velocities, and the possible changes analytical model, with very low computational to those processes. Anthropogenic activities or time, allows for a better understanding of the main long-term natural processes can affect those physical parameters describing the system, helping processes with often drastic and unexpected in the interpretation of the output of the more consequences. The artificial closure of tidal basins complex numerical model. Moreover, the analytical such as for example the Zuiderzee (The model can be used to assess qualitatively the effects Netherlands) in 1932 can result in significant of future changes on the physical system (e.g. increases of the tidal ranges and drastic changes to effects of sea level rise). the hydrodynamics and morphodynamics of the entire basin1. In a similar way, long term natural Materials and Methods trends such as due to sea level rise can affect and modify the tidal propagation of narrow tidal bays The Gulf Of Khambhat and estuaries2. The Gulf of Khambhat (formerly known as the Process-based numerical models are a very Gulf of Cambay) is an inlet of the Arabian Sea useful tool to simulate the dynamics of tidal waves along the west coast of India, in the state of in gulf and estuaries as the main physical processes Gujarat. In the southern side, the gulf is about 230 can be very well represented by those models and km wide and it funnels down moving towards accuracy is generally quite high. On the other hand, north-east direction (Fig. 1). The total length of the the complexity of those models often obscures the gulf is about 250 km. Some major rivers discharge INDIAN J. MAR. SCI., VOL. 43, NO. 7, JULY 2014 into the Gulf a substantial fresh water runoff The model was run in depth averaged mode with a especially during the monsoon seasons: the Mahi, grid coverage shown in Fig. 2, and a spatial the Tapi, the Narmada and the Sabarmati. The resolution ranging approximately between 1,500 m discharges of the Narmada River, which is the at the sea boundary, down to about 100 m in the major river, range between 10,000 to 60,000 m3/s upstream part of the Gulf. during monsoonal floods3. Yearly averaged discharge values were used for The entire gulf is very shallow, with a maximum the four major rivers: water depth of about 30 m. especially the most . Mahi 450 m3/s northern 100 km of the gulf are characterized by . Sabarmati 45 m3/s very large tidal flats and a water depth lower than . Tapi 500 m3/s 10 m. The tidal range in the gulf is the largest along . Narmada 1400 m3/s the entire Indian coastline, peaking to more than 10 m during spring tide and resulting in strong tidal currents of more than 3 m/s4, 5. The high energetic conditions in combination with the large amount of fine sediments brought by the rivers, makes the water always turbid with high suspended load6. 71° 00' 72° 00' 73° 00' KaviBandar 22° 00' Nirma Dam Corridor Dahej 10m 21° 30' Gopinath Hazira Fig. 2. Spatial coverage of the Delft3D grid. 21° 00' Pipavav 10m 10m 10m Diu Analytical model 30m 10m 20m 20° 30' An analytical model for tidal propagation in 20m Daman 30m 30m 20m convergent estuaries has been developed in the 20° 00' 20m Matlab environment. The model is based on the 30m Wadhavan 70° 30' 71° 30' 72° 30' 73° 30' analytical solutions of the continuity and momentum equations for convergent estuaries as Fig. 1. Map of the Gulf of Khambhat described in8. The model is useful to describe the propagation of the main tidal component (usually Model approach M ) under the assumptions that: Process-based numerical model 2 . bottom is horizontal and does not change in A hydrodynamic numerical model of the entire time Gulf was set up based on the Delft3D-FLOW . convective acceleration is neglected modelling system7. The model solves the Navier . linearized friction is used Stokes equations for an incompressible fluid, under . the width b upstream the estuary can be the shallow water and the Boussinesq assumptions. described using an exponential function of The model was implemented at the Coastal and the form b = b e-x with 1/L = Environmental Engineering Division of the 0 b convergence coefficient and L = National Institute of Ocean Technology (NIOT, b converging length scale India). The open boundary at sea was defined Given these assumption the mass balance outside the Gulf at a depth of about 300 m to reduce equation can be expressed as: the number of relevant tidal components (Fig. 2). Moreover, this reduces the interaction of the hu0 uh0 0 propagating and reflected tidal wave at the open tx (1) boundary. Astronomic tidal conditions at the with being the water level with respect to mean boundary were based on the TOPEX/Poseidon u Global database. In particular, 13 astronomic sea level, h0 the channel depth, the cross-section components were used to force the sea boundary: averaged velocity, t the time, and x the horizontal M2, S2, N2, K2, K1, O1, P1, Q1, MF, MM, M4, coordinate along the river. The momentum equation MS4, and MN4. Bathymetry data of the Gulf were can be simplified to: recently collected by NIOT. GIARDINO et al.: TIDAL MODELLING IN THE GULF OF KHAMBHAT ug Bed roughness was specified in terms of mu 0 Nikuradse roughness, with k values respectively tx (2) s equal to 0.001 m and 0.0007 m, corresponding to withg being the acceleration of gravity and m the 1/2 Chezy values Cof about 100 m /s. The small bed Lorentz friction parameter, function of the roughness (high Chezy values) is justified by the characteristic peak velocity, the Chezy coefficient 10 very fine sediments in the entire basin. derived a and the channel depth. As boundary conditions at relationship between the friction coefficient f≈ the ocean side, the tidal amplitude at spring tide 2 (g/C ) and the mud content M: conditions was prescribed. The cross-section f 0.073 / M (3) u averaged river velocity r has also been included in Assuming for M a value equal to 73%, which is the averaged velocity term, in general leading to a realistic estimate for the Gulf of Khambhat, additional frictional and more tidal damping. The values of Cof about 100 m1/2/s can be obtained, as model has also been coupled to an analytical model used in the analytical model. to assess salinity intrusion in estuaries, according to The effect of tidal reflection can also be the work of9. included analytically by adding up the separate In case of bays or estuaries with very different effect of incoming and reflected tidal wave8. bathymetries or convergence lengths along the tidal Non linear effects due to the interaction of propagation direction, those can be included in the different tidal components, effects of limited water model by splitting the geometry of the study area in depth on wave celerity and non linear friction sub-sections with different water depths and/or cannot be accounted for following this approach, convergence lengths, and running the landward part while they are included in the more sophisticated of the model forcing it at the boundary with tidal Delft3D model. and salinity conditions derived from the seaward part.
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