Experimental investigation on rogue waves and their impacts on a vertical cylinder using the Peregrine breather model

This paper presents an experimental investigation on the rogue waves and the corresponding wave forces acting on a vertical cylinder. The waves are modelled using the Peregrine breather solution of the third-order nonlinear Schrödinger equation. The experimental wave elevations are compared with the theoretical solutions, and the behaviours of wave energy distribution and evolution are calculated using the fast Fourier transformation and wavelet transform (WT) methods. The resulting wave forces acting on the vertical cylinder are compared with the numerical results based on potential flow calculations. Moreover, coherence analyses are conducted for the rogue waves and their impact forces acting on the cylinder based on the WT.

[1]  V. Zakharov Collapse of Langmuir Waves , 1972 .

[2]  Jun Zang,et al.  Higher-harmonic focused-wave forces on a vertical cylinder , 2009 .

[3]  Yan‐Chow Ma,et al.  The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation , 1979 .

[4]  Günther Clauss,et al.  Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test , 2013, PloS one.

[5]  Luigi Cavaleri,et al.  Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves , 2006 .

[6]  Odd M. Faltinsen,et al.  Nonlinear wave loads on a slender vertical cylinder , 1995, Journal of Fluid Mechanics.

[7]  J. R. Morison,et al.  The Force Exerted by Surface Waves on Piles , 1950 .

[8]  N. Hoffmann,et al.  Initial wave breaking dynamics of Peregrine-type rogue waves: A numerical and experimental study , 2014, 1401.0949.

[9]  Paul M. Hagemeijer,et al.  A New Model For The Kinematics Of Large Ocean Waves-Application As a Design Wave , 1991 .

[10]  R. Eatock Taylor,et al.  Non-linear analysis of jack-up structures subjected to random waves , 1999 .

[11]  Günther Clauss,et al.  FORMATION OF EXTRAORDINARILY HIGH WAVES IN SPACE AND TIME , 2011 .

[12]  Luigi Cavaleri,et al.  Analysis of the Voyager storm , 2008 .

[13]  John R. Chaplin On Frequency-Focusing Unidirectional Waves , 1996 .

[14]  John R. Chaplin,et al.  Ringing of a vertical cylinder in waves , 1997, Journal of Fluid Mechanics.

[15]  N. K. Shelkovnikov Rogue waves in the ocean , 2014 .

[16]  Hongxiang Xue,et al.  Numerical study of Rogue waves as nonlinear Schrödinger breather solutions under finite water depth , 2015 .

[17]  Chia Chuen Kao,et al.  On the Characteristics of Observed Coastal Freak Waves , 2002 .

[18]  R C MacCamy,et al.  Wave forces on piles: a diffraction theory , 1954 .

[19]  N. Akhmediev,et al.  Waves that appear from nowhere and disappear without a trace , 2009 .

[20]  Mahmoud Ghiasi,et al.  A fully nonlinear wave interaction with an array of submerged cylinders by NURBS numerical wave tank and acceleration potential , 2014 .

[21]  A. Osborne,et al.  Freak waves in random oceanic sea states. , 2001, Physical review letters.

[22]  N. Hoffmann,et al.  Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  C. H. Kim,et al.  Simulation of Draupner Freak Wave Impact Force On a Vertical Truncated Cylinder , 2003 .

[24]  Manuel A. Andrade,et al.  Physical mechanisms of the Rogue Wave phenomenon , 2022 .

[25]  N. Hoffmann,et al.  Rogue wave observation in a water wave tank. , 2011, Physical review letters.

[26]  Marco Klein,et al.  The New Year Wave in a seakeeping basin: Generation, propagation, kinematics and dynamics , 2011 .

[27]  David L. Kriebel,et al.  Simulation of Extreme Waves In a Background Random Sea , 2000 .

[28]  Bin Teng,et al.  Free-surface evolution and wave kinematics for nonlinear uni-directional focused wave groups , 2009 .

[29]  Kharif Christian,et al.  Rogue Waves in the Ocean , 2009 .

[30]  R. C. T. Rainey,et al.  Slender-body expressions for the wave load on offshore structures , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[31]  V. Shrira,et al.  What makes the Peregrine soliton so special as a prototype of freak waves? , 2010 .

[32]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[33]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .