TY - JOUR

T1 - New solutions of the C.S.Y. equation reveal increases in freak wave occurrence

AU - Andrade, David

AU - Stiassnie, Michael

N1 - Funding Information:
This research was supported by the Israel Science Foundation ( Grant 261/17 ).
Funding Information:
The authors are grateful to Dr. R. Stuhlmeier from the University of Plymouth for fruitful discussions related to this work. This research was supported by the Israel Science Foundation (Grant 261/17).
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/9

Y1 - 2020/9

N2 - In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows from the investigation of three related aspects. First, we study the instability of JONSWAP spectra to inhomogeneous disturbances whereby establishing a wider instability region than that predicted by Alber's equation. Second, we study the long time evolution of such instabilities. We observe that, during the evolution, the variance of the free surface elevation and thus, the energy in the wave field, localizes in regions of space and time. Last, we compute the probabilities of encountering freak waves and compare it with predictions obtained from Alber's equation and the Rayleigh distribution.

AB - In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows from the investigation of three related aspects. First, we study the instability of JONSWAP spectra to inhomogeneous disturbances whereby establishing a wider instability region than that predicted by Alber's equation. Second, we study the long time evolution of such instabilities. We observe that, during the evolution, the variance of the free surface elevation and thus, the energy in the wave field, localizes in regions of space and time. Last, we compute the probabilities of encountering freak waves and compare it with predictions obtained from Alber's equation and the Rayleigh distribution.

UR - http://www.scopus.com/inward/record.url?scp=85084764300&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85084764300&partnerID=8YFLogxK

U2 - 10.1016/j.wavemoti.2020.102581

DO - 10.1016/j.wavemoti.2020.102581

M3 - Article

AN - SCOPUS:85084764300

SN - 0165-2125

VL - 97

JO - Wave Motion

JF - Wave Motion

M1 - 102581

ER -