Abstract
Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.
Highlights
Longuet-Higgins [1] deduced the distribution function of wave elements for the first time under the assumption that wave surface displacement is a stationary normal stochastic process and under the narrow spectrum
With the development of ocean observation technology, the measured data and laboratory data proved that the Rayleigh distribution of wave elements is reasonable under the assumption that the wave surface displacement is a normal stochastic process
The new distribution function is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum, and it can fit the observed data more carefully [25,26]
Summary
Longuet-Higgins [1] deduced the distribution function of wave elements for the first time under the assumption that wave surface displacement is a stationary normal stochastic process and under the narrow spectrum. With the development of ocean observation technology, the measured data and laboratory data proved that the Rayleigh distribution of wave elements is reasonable under the assumption that the wave surface displacement is a normal stochastic process. The joint distribution of wave height and period is of great significance in practical applications [13] These joint distribution functions of wave heights and periods are derived under the condition of a narrow spectrum, which has certain limitations in the study of ocean waves [14,15]. The new distribution function is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum, and it can fit the observed data more carefully [25,26] It can be more widely applicable to nonlinear waves in various cases [27,28], owing to the many undetermined parameters it contained. It can reflect the uncertainty of wave elements in some cases and can be better applied in theoretical study and practical application
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
