Numerical modeling of tide-surge interaction along Orissa coast of India

The Orissa coast of India is one of the most vulnerable regions of extreme sea levels associated with severe tropical cyclones. There was extensive loss of life and property due to the October 1999 super cyclone, which devastated large part of the Orissa coast. The shallow nature of the head bay, presence of a large number of deltas formed by major rivers of Orissa such as Mahanadi and Dhamra, and high tidal range are responsible for storm surge flooding in the region. Specifically, rising and falling tidal phases influence the height, duration, and arrival time of peak surge along the coast. The objective of the present study is to evaluate the tide-surge interaction during the 1999 Orissa cyclone by using nonlinear vertically integrated numerical models. The pure tidal solution for the head bay region of the Bay of Bengal provides the initial condition for the fine resolution nested grid Orissa model. However, the feedback from the Orissa model does not affect the head bay model as the study provides a one-way interaction. Numerical experiments are performed to study the tide-surge interaction by considering various relative phases of the tidal waves with the surge-wave produced by 1999 Orissa cyclone. The comparison, although utilizing only the limited estimates of tidal data, appears adequate to assert that the principal features are reproduced correctly.     

Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem

The non-linear stability of the libration pointL ₄ in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL ₄ is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:

A Bay–River Coupled Model for Storm Surge Prediction Along the Andhra Coast of India

The paper describes a two-dimensional bay–river coupled numerical model for storm surges along the Andhra coast of India. The effect of the Krishna and Godavari rivers on the surge development is analysed. A comparative study of the surge generated by a tropical cyclone with and without the inclusion of rivers is done in detail. Three cyclones that struck the Andhra coast in November 1977, May 1990 and November 1996 were used for the simulation studies. It is found that the idealized model without a river overestimates the sea-level elevation as compared to a more realistic bay–river coupled model. The temporal variation of surge values at the mouth of the rivers is also studied for all three cyclone cases. It is found that the effect of the presence of rivers depends on the strength of the cyclone, its point of landfall and the location of the rivers with respect to the landfall point.     

Effect of the Mahanadi River on the Development of Storm Surge Along the Orissa Coast of India: A Numerical Study

River-ocean coupled models are described for the evaluation of the interaction between river discharge and surge development along the Orissa coast of India. The models are used to study the effect of fresh water discharge from the Mahanadi River on the surge response along the Orissa coast due to the October 1999 super cyclone which led to severe flooding of the coastal and delta regions of Orissa. The so-called 1999 Paradip cyclone was one of the most severe cyclones; causing extensive damage to property and loss of lives. The present study emphasizes the impact of the Mahanadi River on overall surge development along the Orissa coast. Therefore, we have developed a location specific fine resolution model for the Orissa coast and coupled it with a one–dimensional river model. The numerical experiments are carried out, both with and without inclusion of fresh water discharge from the river. The bathymetry for the model has been taken from the naval hydrographic charts extending from the south of Orissa to the south of west Bengal. A simple drying scheme has also been included in the model in order to avoid the exposure of land near the coast due to strong negative sea-surface elevations. The simulations with river-ocean coupled models show that the discharge of fresh water carried by the river may modify the surge height in the Bay, especially in the western Bay of Bengal where one of the largest river systems of the east coast of India, the Mahanadi River, joins with the Bay of Bengal. Another dynamic effect of this inlet is the potentially deep inland penetration of the surge originating in the Bay. The model results are in good agreement with the available observations/estimates.     

Effect of sensor modelling methods on computation of 3-D coordinates from Cartosat-1 stereo data

The orbital and the rational polynomial coefficients (RPC) models are the two most commonly used models to compute a three-dimensional coordinates from an image stereo-pair. But it is still confusing that with the identical user provided inputs, which one of these two models provides more accurate digital elevation model (DEM), especially for mountainous terrain. This study aimed to find out the answer by evaluating the impact of used models on the vertical accuracy of DEM extracted from Cartosat-1 stereo data. We used high-accuracy photogrammetric DEM as the reference DEM. Apart from general variations in statistics, surprisingly in a few instances, both the DEMs provided contrasting results, thus proving the significance of this study. The computed root mean square errors and linear error at 90% (LE90) were lower in case of RPC DEM for various classes of slope, aspect and land cover, thus suggesting its better relative accuracy.     

Two‐dimensional physically based finite element runoff model for small agricultural watersheds: I. Model development

Soil erosion by water is the root cause of ecological degradation in the Shiwalik foothills of Northern India. Simulation of runoff and its component processes is a pre‐requisite to develop the management strategies to tackle the problem, successfully. A two‐dimensional physically based distributed numerical model, ROMO2D has been developed to simulate runoff from small agricultural watersheds on an event basis. The model employs the 2‐D Richards equation with sink term to simulate infiltration and soil moisture dynamics in the vadoze zone under variable rainfall conditions, and 2‐D Saint‐Venant equations under the kinematic wave approximation along with Manning's equation as the stage‐discharge equation for runoff routing. The various flow‐governing equations have been solved numerically by employing a Galerkin finite element method for spatial discretization using quadrilateral elements and finite difference techniques for temporal solutions. The ROMO2D computer program has been developed as a class‐based program, coded in C + + in such a way that with minor modifications, the model can be used to simulate runoff on a continuous basis. The model writes output for a runoff hydrograph of each storm. Model development is described in this paper and the results of model testing and field application are to be presented in a subsequent paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Existence of longitudinal waves in pre-stressed anisotropic elastic medium

In a pre-stressed anisotropic elastic medium, three types of quasi-waves propagate along an arbitrary direction. In general, none of the waves is truly longitudinal. The present study finds the specific directions in a pre-stressed anisotropic elastic medium along which longitudinal waves may propagate. This paper demonstrates how the propagation of longitudinal waves is affected by various pre-stresses present in the medium. The study establishes the explicit expressions defining the existence and propagation of longitudinal waves in pre-stressed anisotropic elastic medium. These expressions involve not only the direction and elastic stiffness of the medium, but also the pre-stresses present in the medium. Changes in conditions for the existence of longitudinal waves in orthotropic, monoclinic and triclinic anisotropies are discussed in detail. The most important part of the paper is a practical aspect suggested to calculate the specific directions for the existence of longitudinal waves in pre-stressed anisotropic elastic medium. In this approach, only those parameters are used that can be observed by the receiver in a geophysical experiment of wave propagation. The existence of longitudinal waves has been shown graphically using a numerical example for three types of anisotropic symmetries in elastic medium.