1 Copyright © 2002 by ASME Proceedings of OMAE’02 21 st International Conference on Offshore Mechanics and Arctic Engineering June 23-28, 2002, Oslo, Norway OMAE2002-28620 NONLINEAR WAVE DISTURBANCE AROUND A VERTICAL CIRCULAR COLUMN C.T. Stansberg and H. Braaten Norwegian Marine Technology Research Institute A/S (MARINTEK) Trondheim, Norway ABSTRACT The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m , in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum- frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required. INTRODUCTION The wave field disturbance around single and multiple vertical columns is an essential issue in the prediction of deck clearances under large-volume offshore platforms. This is a classical problem, which was solved analytically for a single bottom-mounted column, assuming linear potential theory, in the early 1950’s (McCamy and Fuchs, 1954). However, experience through a number of studies throughout the recent decade has shown that nonlinear effects may grow siginficant in steep waves. This includes nonlinearities in the incoming waves as well as in the wave-structure interaction. Evidence from experiments is found through a variety of studies on single columns, such as Kriebel (1992, 1993); Niedzwecki & Duggal (1992); Stansberg & Nielsen (2001). For a very large cylinder, some nonlinear effects were also observed in Sterndorff & Skourup (2001), although a considerable part of their measurements were reasonably close to linear. For a multi-leg structure, the experiments in Swan et. al. (1997) showed particular nonlinear effects. Furthermore, several of the experimental studies have shown a significant statistical scatter. Various nonlinear numerical approaches have also been published, see e.g. Büchmann et.al. (1998), Ferrant (1999), ISSC (2000). The leading nonlinear contribution is the second-order correction from diffraction theory. In the present analysis, a second-order diffraction-radiation code (WAMIT, 1995) is applied in a numerical analysis of the single-column problem, and compared to results from a set of systematic and dedicated model scale experiments. The experiments have been described earlier in a ISSC comparative study (ISSC, 2000) and in Stansberg & Nielsen (2001). The comparative study is further described in Nielsen (2002). In the following presentation, data from tests in regular, bi-chromatic as well as irregular waves are included, with wave elevation measurements made in a grid of 32 locations near the column. The work is a continuation of the initial analysis in Stansberg & Nielsen (2001). .A full second-order numerical analysis is made, including quadratic transfer functions (QTFs) for sum-frequency as well as for difference-frequency (set-up / set-down) terms. The purpose of the work is to observe how well the use of this perturbation method can describe the measured nonlinearities, and to provide background material for a discussion on its use in future design. NONLINEAR DIFFRACTION: SOME EXAMPLES FROM MODEL TESTS Measurements of wave enhancement around a 16m- diameter vertical column were observed through systematic model tests and presented in Stansberg & Nielsen (2001). Linear and second-order diffraction theory was compared to the measurements, and predicted trends were fairly well recognized. However, the nonlinearities observed indicate that a further and more detailed investigation is needed, also including more of the data, for a satisfactory description of the