비선형 파동계에서의 파고와 주기 결합 확률분포
Joint Distribution of Wave Crest and its Associated Period in Nonlinear Random Waves
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초록
파고와 주기 결합분포는 그 공학적 가치에도 불구하고, 주기에 대한 해석 모형의 부재로 인해 파고 분포에 비해 상대적으로 소홀히 다루어져, 현재 비선형성이 주기분포에 미치는 영향에 대해서도 서로 다른 의견이 상존한다. 이에 비해 파고 분포의 경우, 많은 노력이 이루어져 성과가 상당하나, 아직 이러한 성과는 파고와 주기 결합분포로 확대되지 못하였다. 본 논문에서는 이러한 문제를 해결하기 위해 먼저 파고와 주기의 결합분포를 조건부 주기 분포 와 파고 분포의 곱으로 정의하였다. 이어 비선형 불규칙 파동계에서의 파고 분포, 임의의 대역폭을 지니는 비선형 불규칙 파랑계에서의 파고분포를 유도하고, 이를 Longuet-Higgins(1975, 1983), Cavanie et al.(1976)의 조건부 주기 확률분포와 결합하여 새로운 파고와 주기 결합분포를 제시하였다. 검증과정은 Wallops 스펙트럼에 기초하여 수치 모 의된 파랑시계열자료와 경사가 1:15인 단조해안에서 진행되는 불규칙 파랑 천수과정 수치모의를 통해 얻은 강비선 형 파랑자료를 활용하여 수행되었으며, 모의 결과 finite banded waves를 대상으로 한 파고 분포와 Cavanie et al. (1976)의 조건부 주기 확률분포를 활용하는 경우 가장 근접한 결과를 얻을 수 있었다.
Abstract
The joint distribution of wave height and period has been maltreated despite of its great engineering value due to the absence of any analytical model for wave period, and as a result, no consensus has been reached about the effect of nonlinearity on these joint distribution. On the other hand, there was a great deal of efforts to study the effects of non-linearity on the wave height distribution over the last decades, and big strides has been made. However, these achievements has not been extended to the joint distribution of wave height and period. In this rationale, we first express the joint distribution of wave height and period as the product of the marginal distribution of wave heights with the conditional distribution of associated periods, and proceed to derive the joint distribution of wave heights and periods utilizing the models of Longuet-Higgins (1975, 1983), and Cavanie et al. (1976) for conditional distribution of wave periods, and height distribution derived in this study. The verification was carried out using numerically simulated data based on the Wallops spectrum, and the nonlinear wave data obtained via the numerical simulation of random waves approaching toward the uniform beach of 1:15 slope. It turns out that the joint distribution based on the height distribution for finite banded nonlinear waves, and Cavanie et al.’s model (1976) is most promising.
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