Hydrodynamic Interactions of Multiple Bodies with Water Waves

Abstract

A hierarchical wave interaction theory is reviewed as an innovative idea for treating hydrodynamic interactions among a great number of bodies rigorously in the framework of linear potential theory. We also introduced experimental results that were obtained using a structure consisting of 64 truncated vertical circular cylinders arranged in a periodical array of 4 rows and 16 columns. From the observation of measured results and their comparison with computed results, the effects of multiple-body interactions on the wave elevation and local steady forces are noted with respect to the wave frequency and the spatial position inside the structure. It is observed that the characteristics of wave interactions clearly change depending on whether the wave frequency is below or above the near trapped-mode frequency. Overall agreement between measured and computed results is very good, although slight differences attributed to viscous effects are observed.

INTRODUCTION

In free-surface hydrodynamic problems of the ship and ocean engineering, there exist a number of examples in which hydrodynamic interactions among multiple bodies are of critical importance. Some of the examples in ship hydrodynamics are the wave interactions between demihulls of a catamaran (Kashiwagi, 1993) and the side-wall interference effects on a ship advancing in waves in a waterway with vertical side walls (Kashiwagi and Ohkusu, 1991). The latter problem can be analyzed by the method of mirror images reflected in both of the parallel side walls, and thus the wave interactions among an infinite number of bodies must be considered. However, since the pattern of ship-generated waves may change drastically depending on the ship’s forward speed U and oscillation frequency ω in waves, it is said that the effect of wave interactions becomes less important when the value of parameter τ=Uω/g (where g is the gravitational acceleration) is larger than 1/4.

On the other hand, looking at ocean-engineering problems, the forward speed of an ocean structure is normally zero or very small. Thus the effects of wave interactions must be taken into account in the wave-related hydrodynamic analyses for a structure with several surface-piercing columns that support an upper deck (e.g. Newman, 2001). However, when the number of interacting bodies is not large, no special theoretical treatment is needed, and a conventional free-surface Green-function method, for instance, can be applied directly to the entirety of interacting bodies as a single structure.