Proceedings of the Thirty-first (2021) International Ocean and Polar Engineering Conference
Rhodes, Greece, June 20 – 25, 2021
Copyright © 2021 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-82-1; ISSN 1098-6189

www.isope.org

Reproduction of Wave Field from Spatiotemporal Discontinuous Wave Data
Etsuro Okuyama
Akishima Laboratories (Mitsui Zosen ) Inc.
Akishima, Tokyo, Japan

Munehiko Minoura
Department of Naval architecture and Ocean Engineering, Osaka University
Suita, Osaka, JapanAs a possibility of the experimental wave basin in the future, it will be
required to spatiotemporally control and reproduce the wave field
actually encountered by the ship. This rationale is that ships and marine
structures have come to be equipped with monitoring devices, and it has
become possible to obtain video data of waves encountered and ship
motion and response data at that time. Many of the video images of ocean
waves taken on board capture the wave motion from concentration todiffusion, which is dangerous for ships. The main purpose of this device
is to use for the performance evaluation, safety assurance, maintenanceplan, etc. in the ship operation. On the other hand, it is also possible tosupport safe operation by predicting one period ahead from monitoring
data, and to reproduce dangerous wave encounters and accidents by postanalysis and provide feedback for future operations.

ABSTRACT
We propose a method to reproduce the encountered ocean wave field bya ship in the experimental wave basin from the wave elevation observed
on board of a ship discontiguously in space and time, based on the linear
theory. The mathematical wave model is based on the Bessel function
for a circular wave basin and estimated its parameters by the least square
method. Wave elevation is assumed to be observed by the 3D camera
and image analysis system equipped on board. This method and themathematical model are validated with the results of numericalcalculations and tank experiments.

KEY WORDS: Element absorbing wave maker, Circular wave basin,
Bessel function, Stereo camera system, On-board monitoring system,
Least square method, Arbitrary wave field.

In this paper, we propose a method to reproduce the spatiotemporally
continuous ocean wave field in the experimental wave basin from thespatiotemporally discontiguous measured ocean wave elevation data.
The purpose of this proposal is to reproduce dangerous wave encounters
and accidents by post-analysis and provide feedback for future
operations. Wave elevation are assumed to be observed at conspicuous
points on the wave surface such as peaks of waves by the 3D camera andimage analysis system equipped on board. These conspicuous points arevariable depending on the wave surface, so that wave elevation data
become discontiguous spatiotemporally. Due to this discontiguousness,the Fourier analysis method is not applicable for identifying parametersof the mathematical wave model. Therefore, we estimate the parametersof the mathematical wave model parameters by the least square method
instead by the Fourier analysis method.

INTRODUCTION
Naito et al. (1999) developed the circular wave basin (AMOEBA) with
50 element absorbing wave-makers installed all around the wave basin.
Although it is a small basin with a diameter of 1.6 m and a water depthof 0.25 m, each wave-maker can be controlled independently, andarbitrary wave field can be reproduced in the basin. After that, large wave
basins with the same concept were constructed at the National Maritime
Research Institute of Japan (Tanizawa, 2013), the University of Sao
Paulo (de Mello et al., 2013), the University of Edinburgh (Draycott, Set al., 2015), etc., and are practically used for performance evaluation
and research and development of ships and marine structures.

The mathematical model of the wave field consists of the Bessel function
as the base considering the reproduction in a circular wave basin withelement absorbing wave-makers installed around it, and it is in a linear
assumption at infinite water depth. Within the linear assumption, weconstruct a method for reproducing the spatiotemporally contiguous
wave field in a wave basin, and validate it by numerical simulation andtank experiment.

All of the experimental wave basins are characterized by being able togenerate arbitrary wave field due to their high wave-making performance,and can generate time-controlled waves at fixed points or stochasticallycontrolled multidirectional irregular waves. As for ships, the former ismainly used to investigate maximal ship motion and structural response.
The latter is used to estimate the mean added resistance in waves by thetowing experiment or the mean added ship propulsive power in waves
by the free running experiment.

In the tank experiment, the position and displacement of objects floating

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