Method for Calculating Forces Produced by Irregular Waves

Abstract

This new method for calculating wave forces on offshore structures is based on an extension of Airy theory for two-dimensional waves and uses a linear filtering technique to calculate wave forces as a function of time for wave profiles of arbitrary shape and length. Introduction Interest in wave-force predictions has been increasing in recent years with the increasing worldwide investment in offshore operations and the movement into deeper water. The larger structures required in deeper water increase the need for rapid and accurate waveforce predictions. This paper presents a method for computing wave forces from an ocean-wave profile by a linear filtering technique and compares these computed forces with measurements. The linear filter employed is developed from a modification of small-amplitude wave theory suggested by wave-tank studies and used to calculate water velocities and accelerations. In the linear filtering method, a wave train of any length and any degree of irregularity can be used in design and dynamic studies of offshore structures. Further, the change of the wave profile shape with time (dispersion) can be allowed for. Velocities and accelerations calculated with the linear filter and introduced into an equation proposed by Morison et al. permits calculation of wave forces. Force coefficients required in Morison's equation were determined by fitting calculated forces to observed hurricane wave-force measurements. Consequently, the force coefficients should be used only with the calculation procedures presented in this paper; further, their application has been limited to calculation of forces on members similar in size and surface properties to the test member used to obtain the measured properties to the test member used to obtain the measured forces. The force predictions are compared with force measurements made in about 400 waves at various heights along a 44-in.-diameter piling in 99 ft of water during Hurricane Carla in 1961. The procedure gives acceptable prediction of maximum forces at all heights above bottom. Force profiles in the four largest measured waves are reproduced with reasonable fidelity, and the peak forces in these largest waves are closely reproduced. Additional force measurements made in shallow water (34 ft) are not referred to in this paper. The wave theory used is less applicable in shallow water, leading to considerable scatter in fitting results. The force measurements indicate that wave forces fall off sharply near the surface of the water. Reproduction of the actual flow regime near the wave surface requires further modification of any way theory. This additional modification is not discussed here. Procedure Used to Predict Wave Forces Procedure Used to Predict Wave Forces Force Equation The horizontal force per foot of vertical piling length is calculated as a function of time t and height z above the ocean bottom as: (1) Eq. 1, proposed by Morison et al., represents the total force as a sum of drag and inertial forces. JPT P. 359

Second Generation Intact Stability Criteria: on the validation of codes for direct stability assessment in the framework of an example application

“…This characteristic is in line with the requirements proposed in [9]. Using an approach along the line in [27], particular attention was given to embed a suitable stretching of the pressure and particle's velocity fields in order to guarantee, in particular, zero-pressure at the free surface (see discussion on this issue in [30]). Radiation terms (leading to added mass and wave damping) are based on linear hydrodynamic pre-calculations.…”

“…It is worth mentioning here, as a comment, that the Airy model requires proper stretching (e.g. [27,28,29]) before being consistently usable for large amplitude motion simulations (e.g. [22,30]) otherwise the zero-pressure condition at the free surface cannot be properly enforced.…”

Design of support structures for offshore wind turbines

“…Several methods have been suggested to correct this. One of the most commonly used methods is Wheeler stretching [11] [12]. The wave kinematics profile over the water depth is determined for every time step.…”

Cylinder loading in transient motion representing flow under a wave group

“…Even for steep waves on deep water, the return current is small, typically less than 10 per cent of the large linear kinematics component close to the free surface, so neglecting it is a reasonable first approximation. Although this is crude, many offshore structures have been designed using 'Wheeler stretching' of the linear kinematics profile, see Wheeler (1970), so we consider that the motions defined by equations (2.2) and (2.3) based on linear deep water wave kinematics are an appropriate starting point.…”