R.C. Ertekin

Waves caused by a moving disturbance in a shallow channel of finite width

The flow created by an impulsively started pressure distribution travelling at a constant velocity in a shallow channel is investigated. The restricted Green-Naghdi theory of fluid sheets is used to perform the three-dimensional calculations. The results show remarkable similarity to model tests. In particular, these calculations predict the periodic generation of two-dimensional solitons in front of and travelling faster than the disturbance if the disturbance is large enough. Behind the disturbance a complicated, doubly corrugated set of waves is formed. The computations also predict that periodic creation of solitons is accompanied by a correspondingly periodic oscillation of the wave drag, as well as a dramatic increase in the mean wave drag.

A derivation of the Green-Naghdi equations for irrotational flows

A new derivation of the Green-Naghdi (GN) equations for `sheet-like flows is made by use of the principle of virtual work. Divergence-free virtual displacements are used to formulate the momentum equations weakly. This results in the elimination of the internal pressure from the GN equations. As is well-known in particle dynamics, the principle of virtual work can be integrated to obtain Hamiltons principle. These integrations can be performed in a straightforward manner when the Lagrangian description of fluid motion is adopted. When Hamiltons principle is written in an Eulerian reference frame, terms must be added to the Lagrangian to impose the Lin constraint to account for the difference between the Lagrangian and Eulerian variables (Lin). If, however, the Lin constraint is omitted, the scope of Hamiltons principle is confined to irrotational flows (Bretherton). This restricted Hamiltons principle is used to derive the new GN equations for irrotational flows with the same kinematic approximation as in the original derivation of the GN equations. The resulting new hierarchy of governing equations for irrotational flows (referred to herein as the IGN equations) has a considerably simpler structure than the corresponding hierarchy of the original GN governing equations that were not limited to irrotational flows. Finally, it will be shown that the conservation of both the in-sheet and cross-sheet circulation is satisfied more strongly by the IGN equations than by the original GN equations.

A Strongly-Nonlinear Model for Water Waves in Water of Variable Depth—The Irrotational Green-Naghdi Model

Summary and Conclusions The Irrotational Green-Naghdi equations are derived for finitewater-depth conditions, and tested numerically to show their self-convergence and accuracy. The linear and nonlinear dispersion ofthe permanent progressive wave solutions of the IGN equationsconverged to known exact solutions as the Level of the equationsincreases. The numerical solution of the IGN equations for un-steady problems, such as the run-up of solitary waves and nonlin-ear shoaling over a sloping beach, also converged. It appears thatthe IGN Level 3 equations can provide very accurate solutions formost engineering problems. The IGN Level 2 equations showedcomparable accuracy with the optimal WKGS equation set, whichis known to be the most accurate Boussinesq-type model.Once the accuracy of the IGN equations at each level is iden-tified, the level can be optimally chosen in future application ofthe model to various water-wave problems. Acknowledgment JWK and RCE have been supported by the ONR, Grant No.N000114-98-1-0800; the Program Manager was Dr. C. LinwoodVincent. JWK was also supported by Korea Science and Engi-neering Foundation for an initial stage of the present work. KJBwas supported by Grant No. R01-2000-00321 from the KoreaScience and Engineering Foundation. These grants are gratefullyacknowledged ~SOEST No. 6056!.

APPROXIMATE METHODS FOR DYNAMIC RESPONSE OF MULTI-MODULE FLOATING STRUCTURES

Abstract Two-dimensional and three-dimensional approximate hydroelasticity theories are used to predict the dynamic response of 5- and 16-module very large floating structures in regular waves. For the two-dimensional approach, strip theory is combined with a beam model of the structure to determine the dynamic response. However, the fluid forces from strip theory are augmented with ‘surge’ forces calculated from Morisons equation. For the three-dimensional approach, a rigid module, flexible connector structural model is used with fluid loading obtained with the three-dimensional double composite source distribution technique. Fluid-structure interaction effects are studied and connector moments are obtained. These approximate methods of hydroelastic analysis offer alternatives to the more computationally demanding, fully three-dimensional flexible module, flexible connector model in which linear potential theory is used.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder

A three-dimensional time domain approach is used to study nonlinear wave diffraction by a fixed, vertical circular-cylinder that extends to the sea floor. In this approach, the development of the flow can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any instant of time is obtained by the boundary-element method. In the numerical calculations, the exact body-boundary condition is satisfied on the instantaneous wetted surface of the cylinder, and the extended Sommerfield condition is used as the numerical radiation condition. The fourth-order Adams-Bashford method is employed in the time stepping scheme. Calculations are done to obtain nonlinear diffraction of solitary waves and Stokes second-order waves by a vertical circular cylinder. Numerical results are compared with available linear and second-order wave-force predictions for some given wave-height and wave-length conditions, and also with experimental data.

A comparative study of RMFC and FEA models for the wave-induced response of a MOB

Abstract A comparative study of the linear, wave-induced response of a 5-module mobile offshore base (MOB) based on two structural models is reported herein. The lumped parameter, rigid module, flexible connector (RMFC) model and a more detailed finite element shell model were used. The 1500 m ×152 m MOB corresponds to McDermotts design concept, where the modules are hinge-connected at the deck. The wave-induced response was determined based on linear hydroelasticity, which involves linear potential theory for the fluid forces. The response in both regular and irregular seas is compared. The results show that the simplified RMFC model can predict the response very well if the natural frequencies and associated normal modes correspond well to the FEA models frequencies and modes. Under these conditions, the simpler RMFC model, which is especially useful for preliminary and conceptual design during which parametric studies are carried out, can therefore be used with a good deal of confidence.

Computationally efficient techniques in the hydroelasticity analysis of very large floating structures

Abstract Two techniques are introduced in the three-dimensional hydroelasticity theory to increase the computational efficiency for the determination of the dynamic response of very large floating structures (VLFS). One technique is related to the convergence of the Green function and its derivatives, namely the introduction of a criterion used to truncate the influence of the Green function and its derivatives. The other involves using an iterative sparse solver for the linear system of equations. The principle motivation behind the application of these two techniques stems from the fact that a source makes a very small contribution to the potential at a point “far away” from the source point. By employing these two techniques in the hydroelastic analysis of a VLFS, the CPU time and required storage are considerably reduced and therefore it is now possible to analyze the dynamics of a VLFS as large as a floating airport by using the three-dimensional panel method.

Hydroelasticity of an infinitely long plate in oblique waves: Linear Green-Naghdi theory

The Level I Green-Naghdi (GN) theory is developed, within the assumptions of linearity, to analyse the hydroelastic response of an infinitely long elastic plate of finite width. The plate is freely floating on the free surface of finite depth and in regular oblique waves. An equation of motion is obtained that is similar to the shallow-water wave equation of Stoker, but which possesses an improved dispersion relation and includes the added-mass force due to the vertical motion of the fluid column. Comparisons with the available experimental data for the special case of beam seas show good agreement with the present theory. An explicit solution is also obtained when the plate is very wide. A local analysis near the critical wave number is made for the solution, and it is shown that the deflection of the plate, not necessarily at its edges, can be made arbitrarily large by increasing the width of the plate.

Time-domain simulation of large-amplitude response of floating platforms

Abstract Two numerical simulation models to predict large-amplitude motions of floating platforms are presented. The first method is based on the application of the relative-velocity formulation of Morisons equation for force calculations. The second method developed in this work uses the three-dimensional potential theory in time domain. In this method, both the Froude-Krylov and scattering forces are calculated by considering finite wave amplitude effects in random waves. The effect of various nonlinearities on the low-frequency motions and high-frequency tether-tension response of a tension leg platform are studied using these simulation models in conjunction with power spectral methods. The presence of current and the nonlinear drag force are observed to have a significant effect on the low-frequency motions and tether tensions.

The Calculation of the Instability Criterion for a Uniform Viscous Flow Past an Oil Boom

An important problem in oil spill containment by booms is the instability of the oil-water interface at the boom. This instability, which represents the conditions under which oil can escape under the boom, is investigated. A viscous flow model for thin slicks in two dimensions is developed. To understand the effect of viscosity on the instability criterion, the full Navier-Stokes equations are solved by the fractional-step method in time-domain to determine the pressure gradients along the boom. The numerically obtained viscous instability criterion is then compared with the potential flow and experimentally determined instability criteria. Analytical instability formulas for potential flows are based on the velocity potentials for attached and detached flows due to uniform current past a flat plate in finite and infinite water depths. The results show that the viscous flow model predicts a larger region of stability. It is numerically determined from the instability criterion that the oil droplets at the boom between the free surface and down to about 40 percent of the boom height can never escape, regardless of the current strength. It is also shown that the instability criterion depends weakly on the high Reynolds number. Reanalysis of the available experimental data confirms thesemorexa0» findings.«xa0less