On the Wave Pattern Analysis by Means of Transverse Cut Method for Asymmetrical Ship Waves : A Proposition of the Fourier Transform Method by Means of a Sheet of Transverse Wave Profile

Abstract

In this paper, a new transverse cut method in the type of Fourier transform is proposed on the field of wave pattern analysis. If this new method is applied for the analysis of asymmetrical ship waves, the amplitude functions of free wave is able to determine by use of only a sheet of transverse wave profile. That is to say, the amplitude function of elementary waves propagated toward the opposite side of each measured side are obtained in asymmetrical wavy flow field, when we transform a sheet of wave profile measured along the transverse cut perpendicular to ship's cource from centre line to infinity sideways both port and starboad sides by means of Fourier integral. The present methed of asymmetrical wave pattern analysis is applied to theoretical wave pattern generated by a submerged point doublet with oblique axis in order to confirm the reasonableness of present method. The effects of radiation condition of ship waves on the equation of wave pattern analysis are also mathematically studied in the case that the longitudinal position of transverse cut goes to infinity rearwards. Furthermore, the relationship between the newly proposed method and the ordinary method is theoretically showed on the transverse cutting wave pattern analysis in the form of Fourier transform and is numerically illustrated on the base of analysis for theoretical wave pattern generated by a submerged point source.