N. Jothi Shankar

Two- and three-dimensional oil spill model for coastal waters

This paper presents the development and application of two-dimensional and three-dimensional oil trajectory and fate models for coastal waters. In the two-dimensional model, the oil slick is divided into a number of small grids and the properties of each grid due to spreading, advection, turbulent diffusion, evaporation and dissolution are studied. This model can predict the movement of the oil slick on the water surface. In order to simulate the distribution of oil particles in the water column, a three-dimensional oil fate model is developed based on the mass transport equation and the concentration distribution of oil particles can be solved. A comparison of numerical results with the observed data shows good conformity.

Estimation of incident and reflected waves in regular wave experiments

Abstract This paper presents a laboratory technique for measurement of reflected waves by a submerged horizontal plate. A simple method is proposed to decompose the composite wave record obtained from the wave reflection experiments in the wave flume. The data collected were used to compute the reflected wave height by means of two and three probe methods proposed by other investigators and compared with the directly computed reflected wave using the measured incident wave. The experiment was carried out for a horizontal plate of 1 m length spanning the full width of the flume with wave periods ranging from 0.8 to 1.8 sec with 0.1 sec increments and wave heights of 5, 10 and 15 cm. The methods using two and three probes with phase measurement yield better results than the three probe method without phase measurement, and in general they have a wider range of application. The method using three probes without the phase measurement generally fails due to numerical instability of the scheme. The results obtained by the proposed method are compared with the two and three probe methods and a comparative analysis of the four methods is presented and discussed.

Wave forces on submarine pipelines near a plane boundary

Abstract Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.

Forces on a smooth submarine pipeline in random waves — A comparative study

Abstract Forces on a smooth submarine pipeline, fixed horizontally near a plane boundary, have been investigated under random wave conditions. The submarine pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) at various energy levels. The water particle kinematics were computed based on the linear random wave model and the Morison equation was chosen as the wave force predictor model. The inline hydrodynamic coefficients of drag and inertia were evaluated using two different methods, one in the frequency domain and the other in the time domain. Five mathematical formulations were considered for the analysis of transverse wave forces and these were compared in terms of the correlation coefficient. The transverse force was also analyzed in terms of the transverse root mean square (rms) coefficient. The inline hydrodynamic coefficients of drag and inertia and the transverse rms coefficient were correlated with the Keulegan-Carpenter number or period parameter, the relative clearance of the pipeline from the bed and the depth parameter. Finally, the results of the random wave tests were compared with those of regular waves under similar pipeline conditions.

Wave forces on large offshore pipelines

Abstract A laboratory investigation of wave forces induced by a regular train of waves on a large pipeline resting on the bed and at various clearances from the bed is presented. From considerations of dimensional analysis horizontal and vertical components of wave forces acting on the pipeline are expressed as force coefficients which are shown to be functions mainly of H/2a, gT 2 /2a, d/a and e/2a . A simple unseparated flow model based on potential flow theory and Morisons equation is presented for evaluating the maximum forces on the pipeline. The experimental results are com3ared with the theoretical results and data from existing literature. Based on the experimental results, hydrodynamic coefficients C M and C L have been evaluated

Wave induced pressures and forces on a fixed submerged inclined plate

Abstract The diffraction of water waves by a submerged fixed inclined plate is modelled using the finite element method (FEM). Wave induced pressures and forces on the submerged fixed inclined plate due to incident monochromatic waves are analysed using the finite element model. The fluid domain is discretised using 8 node isoparametric elements with 3 node quadratic line elements on the free surface, bed and radiation boundaries. The accuracy of the numerical technique is demonstrated by comparing the FEM results with the analytical solution obtained by long wave solution for a thin submerged fixed horizontal plate in shallow water. The horizontal and vertical force coefficients are computed for various wave periods and inclinations of the plate. The reflection and transmission coefficients are also computed and presented for various submergence depths. The possible use of the submerged inclined plate as a breakwater and its advantages over the horizontal plate are discussed.

A boundary-fitted grid model for tidal motions: Orthogonal coordinates generation in 2-D embodying Singapore coastal waters

Abstract This paper proposes a computational procedure for the generation of an orthogonal coordinate system based on the existing curvilinear coordinates generation techniques. The paper is divided into three sections. Firstly a brief review of the curvilinear coordinates generation by the elliptic grid generation technique along with the curvature constraint that governs the metric of a coordinate system is presented. A procedure for the generation of an orthogonal coordinate system is also outlined. Secondly numerical solution for the grid generation system suggested in the present grid generation procedure is described. The proposed grid generation procedure is adopted for the generation of an orthogonal coordinate system for the 2-D domain of Singapore coastal waters. The generated grid demonstrates very satisfactory results.

Regular and random wave pressures around large diameter submarine pipeline near ocean bed

The submarine pipeline fixed horizontally near a simulated ocean bed and parallel to the crests of the oncoming regular waves is formulated as a boundary value problem utilizing Greens second identity formulation for potential functions. Numerical results are obtained for the hydrodynamic pressures that act around the circumference of the pipeline in a finite water depth for salient pressure ports by solving the resulting integral equation. The normalized maximum pressure at each pressure port is correlated with scattering parameter, gap ratio of the pipeline from the ocean bed and depth parameter. An experimental investigation has also been carried out on the regular and random wave induced hydrodynamic pressures around a horizontal submarine pipeline placed at various elevations or gaps from the simulated ocean bed. In the random wave pressure experiments, the pipeline was subjected to random waves with Pierson- Moskowitz spectrum (P-M spectrum) at various energy levels to achieve different significant...

Root mean square force coefficients for submarine pipelines

Abstract An experimental investigation has been carried out on forces induced by regular and random waves on submarine pipelines placed near a plane boundary. The inline and transverse forces are analysed in terms of combined root mean square (rms) hydrodynamic coefficient. The total rms coefficient is correlated with Keulegan-Carpenter number or period parameter and relative clearance of the pipeline from the plane boundary. The pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) in the random wave force tests. The time histories of water particle kinematics are generated using the linear numerical transforms. This paper also reports the effect of depth parameter on the total rms coefficient. The results of the random wave force tests are finally compared with those of regular waves.

WAVE LOADS ON LARGE VERTICAL CYLINDERS: A DESIGN METHOD

Abstract The finite element method based on linear diffraction theory proposed by Zienkiewicz and Bettess (1977) has been used to compute wave loads and moments about the bed of surface piercing cylinders of circular, square, rectangular and elliptical sections for different angles of wave incidence. On the basis of the results obtained, a design method is presented in the form of simple design charts for estimating wave forces and moments on large cylinders of arbitrary sections. The numerical solutions obtained have been checked for their validity by comparing with other theoretical solutions and experimental data. Further the application of the design method to a case study shows good correlation with experimental and other theoretical solutions.