Description Of The UK Christchurch Bay Wave Force Project And Some Initial Results-Part 2

Abstract

Abstract Preliminary results of spectral and Preliminary results of spectral and probabilistic analysis of wave and wave-induced loads probabilistic analysis of wave and wave-induced loads on the main tower and wave staff of the Christchurch Bay experiments are presented. The results obtained to date show reasonable agreement with linear random-wave solutions and the influence of the non-linear drag element of the loading is apparent. The data needs to be expanded with particular reference to fluid kinematics in the presence of waves and currents, and their effect on wave loading. Introduction Part II of this paper discusses the results obtained to date from an analysis of the Christchurch Bay data in spectral and probabilistic terms. Again, it is noted that the results presented here are interim in that further analysis and cross-checking of the data is continuing. 2. THEORETICAL BACKGROUND 2.1 The Wave Conditions A method of predicting wave induced forces on offshore structures which has found increasing application to design problems in recent years is based on the concept of considering the wave motion as a stationary random process. Incident wave conditions are expressed in terms of the surface-elevation spectrum, Sn(w), such as the Pierson-Moskowitz or Jonswap formulations. These Pierson-Moskowitz or Jonswap formulations. These can be related to the usual parametric descriptions of wave conditions in terms of the significant wave height, H1/3, and the zero-crossing period, Tz, and it is sometimes appropriate to use a 'spreading-function' giving a two-dimensional spectrum Sn(w, 0) representing a three-dimensional sea-state. In parallel with the spectral formulation are the probabilistic properties of the surface-elevation which, under certain assumptions, can be considered as a Gaussian process with probability density function, (p.d.f): (1) It has been shown by several authors, notably Longuet-Higgins, that for certain conditions the p.d.f of wave-height is approximated by the Rayleigh density function which in cumulative form is given by: (2) Thus the wave condition can be described by the spectrum, the Gaussian p.d.f of surface-elevation and the Rayleigh p.d.f of wave height. 2.2 The Loading Model Morison's equation for the in-line horizontal force per unit length on a vertical cylinder represents the total force as the sum of a non-linear drag component and a linear inertial component. (3) where being the density of sea-water; Cd and Cm are the drag and inertia coefficients, u is the horizontal water particle velocity and u is the acceleration. particle velocity and u is the acceleration. There are obviously deficiencies in this representation, for example, transverse forces are not included and the coefficients Cd and Cm are considered to be constants. However, the wide-spread use of the Morison equation in design and, as yet, the absence of a reliable alternative justify its use as the 'core' of spectral and probabilistic extentions. P. 187