Numerical study on the effects of uneven bottom topography on freak waves

Abstract A numerical model is built by using an improved VOF method coupled with an incompressible Navier–Stokes solver. Exploiting the model, the freak wave formation due to the dispersive focusing mechanism is investigated numerically without uneven bottoms and in presence of uneven bottoms. During the freak wave transformation over an uneven bottom in finite water, combined effects of shoaling, refraction and reflection can modify the external characteristics of freak waves, and also can complicate the energy transfers. Furthermore, wavelet analysis method is adopted to analyze the behavior of the instantaneous energy structure of freak waves. It is found that when the bottoms vary in height, the external characteristic parameters and high frequency energy show a similar trend, but the value may be quite different due to the difference in local characteristic of the bottom.

[1]  Efim Pelinovsky,et al.  Freak waves under the action of wind: experiments and simulations , 2006 .

[2]  Nobuhito Mori,et al.  Analysis of freak wave measurements in the Sea of Japan , 2002 .

[3]  Stephan T. Grilli,et al.  A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom , 2001 .

[4]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[5]  Paul Stansell,et al.  Distributions of freak wave heights measured in the North Sea , 2004 .

[6]  Yu-xiu Yu,et al.  An experimental and numerical study of the freak wave speed , 2013, Acta Oceanologica Sinica.

[7]  Efim Pelinovsky,et al.  Physical Mechanisms of the Rogue Wave Phenomenon , 2003 .

[8]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[9]  Chiang C. Mei,et al.  The transformation of a solitary wave over an uneven bottom , 1969, Journal of Fluid Mechanics.

[10]  Chin H. Wu,et al.  A new efficient 3D non-hydrostatic free-surface flow model for simulating water wave motions , 2006 .

[11]  Alexander V. Boukhanovsky,et al.  FREAK WAVE GENERATION AND THEIR PROBABILITY , 2004 .

[12]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[13]  Nobuhito Mori,et al.  Wavelet Spectrum of Freak Waves in the Ocean , 2000 .

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

[15]  Aifeng Yao,et al.  Laboratory measurements of limiting freak waves on currents , 2004 .

[17]  Cheng Cui,et al.  Research on the Time-Frequency Energy Structure of Freak Wave Generation and Evolution , 2011 .

[18]  Paul Taylor,et al.  The shape of large surface waves on the open sea and the Draupner New Year wave , 2004 .

[19]  C. Soares,et al.  Non-linearity and non-stationarity of the New Year abnormal wave , 2008 .

[20]  Bing Ren,et al.  Numerical simulation of random wave slamming on structures in the splash zone , 2004 .

[21]  Paul Stansell,et al.  Distributions of extreme wave, crest and trough heights measured in the North Sea , 2005 .

[22]  Philippe Fraunié,et al.  Numerical analysis of the internal kinematics and dynamics of three-dimensional breaking waves on slopes , 2003 .

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

[24]  T. Soomere,et al.  Soliton interaction as a possible model for extreme waves in shallow water , 2003 .