NONLINEAR INERTIAL LOADING. PART I: ACCELERATIONS IN STEEP 2-D WATER WAVES

Abstract

This paper reports on a new series of laboratory observations in which both the unsteady and the convective components of the water particle acceleration arising beneath an extreme two-dimensional transient wave were determined. The waveform investigated was produced by focusing frequency components within an irregular wave train, such that a large number of zero up-crossings arise at one point in space and time. For a given underlying set of frequency components, this produces an extreme event that has the maximum wave slope and therefore also the largest horizontal water particle accelerations. Spectral analysis, based upon the water surface elevation measured at the focal location, confirms that there are significant transfers of energy into the high-frequency components. Neither a linear random wave theory nor a steady nonlinear wave theory, both of which are commonly used in design applications, are able to correctly model these frequency components. As a result, such solutions provide a poor description of the large unsteady accelerations arising close to the water surface. Furthermore, since they are also unable to model the spatial evolution of the wave group, inaccurate predictions of the convective accelerations result. In contrast, a fully nonlinear unsteady wave theory, similar to that originally proposed by Fenton & Rienecker (1980), provides a good description of the laboratory data. To assess the importance of the nonlinear accelerations the inertia forces acting on a vertical, surface-piercing, cylinder are calculated and comparisons made with the nonlinear slender body forces identified by Rainey (1989, 1995). These comparisons confirm the importance of the applied wave model and suggest that the dominant contribution to the high-frequency forcing arises due to the nonlinearity of the wave motion. These results have applications in Offshore Engineering where transient structural deflections, occurring at frequencies well above the wave frequency, have been observed in a number of deep-water structures.