Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T05:16:57.751Z Has data issue: false hasContentIssue false
  • English
  • Français

Extreme wave statistics of long-crested irregular waves over a shoal

Published online by Cambridge University Press:  11 November 2019

Karsten Trulsen Open the ORCID record for Karsten Trulsen [Opens in a new window] ,
Anne Raustøl ,
Stian Jorde  and
Lisa Bæverfjord Rye
Karsten Trulsen*
Affiliation:
Department of Mathematics, University of Oslo, 0371 Oslo, Norway
Anne Raustøl
Affiliation:
Department of Mathematics, University of Oslo, 0371 Oslo, Norway
Stian Jorde
Affiliation:
Department of Mathematics, University of Oslo, 0371 Oslo, Norway
Lisa Bæverfjord Rye
Affiliation:
Department of Mathematics, University of Oslo, 0371 Oslo, Norway
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We report laboratory experiments of long-crested irregular water surface waves propagating over a shoal. For a sufficiently shallow shoal we find that the surface elevation can have a local maximum of skewness and kurtosis above the shallower part of the shoal close to the edge on the incoming side, and a local minimum of skewness over the downward slope on the lee side of the shoal. We find that the horizontal fluid velocity can have a local maximum and minimum of skewness at the same locations as those for the surface elevation. However, the kurtosis of the horizontal fluid velocity can have a local maximum over the downward slope on the lee side of the shoal, different from the location of the maximum of kurtosis of the surface elevation.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 882 , 10 January 2020 , R2
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beji, S. & Battjes, J. A. 1993 Experimental investigation of wave propagation over a bar. Coast. Engng 19, 151–162.Google Scholar
Beji, S. & Battjes, J. A. 1994 Numerical simulation of nonlinear wave propagation over a bar. Coast. Engng 23, 1–16.Google Scholar
Bitner, E. M. 1980 Non-linear effects of the statistical model of shallow-water wind waves. Appl. Ocean Res. 2, 63–73.Google Scholar
Bolles, C. T., Speer, K. & Moore, M. N. J. 2019 Anomalous wave statisics induced by abrupt depth change. Phys. Rev. Fluids 4, 011801.Google Scholar
Cherneva, Z., Petrova, P., Andreeva, N. & Guedes Soares, C. 2005 Probability distributions of peaks, troughs and heights of wind waves measured in the Black Sea coastal zone. Coast. Engng 52, 599–615.Google Scholar
Ducrozet, G. & Gouin, M. 2017 Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. J. Ocean Engng Mar. Energy 3, 309–324.Google Scholar
Goda, Y. 2000 Random Seas and Design of Maritime Structures, p. 443. World Scientific.Google Scholar
Gramstad, O., Zeng, H., Trulsen, K. & Pedersen, G. K. 2013 Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Phys. Fluids 25, 122103.Google Scholar
Grue, J. 1992 Nonlinear water waves at a submerged obstacle or bottom topography. J. Fluid Mech. 244, 455–476.Google Scholar
Jorde, S.2018 Kinematikken i bølger over en grunne. Master’s thesis, University of Oslo.Google Scholar
Kashima, H., Hirayama, K. & Mori, N. 2014 Estimation of freak wave occurrence from deep to shallow water regions. Coast. Engng Proc. 1 (34), 36.Google Scholar
Lamb, H. 1932 Hydrodynamics, p. 738. Dover.Google Scholar
Ma, Y., Dong, G. & Ma, X. 2014 Experimental study of statistics of random waves propagating over a bar. Coast. Engng Proc. 1 (34), 30.Google Scholar
Majda, A. J., Moore, M. N. J. & Qi, D. 2019 Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change. Proc. Natl Acad. Sci. USA 116, 3982–3987.Google Scholar
Massel, S. R. 1996 Ocean Surface Waves: Their Physics and Prediction, p. 491. World Scientific.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, p. 336. Cambridge University Press.Google Scholar
Raustøl, A.2014 Freake bølger over variabelt dyp. Master’s thesis, University of Oslo.Google Scholar
Sergeeva, A., Pelinovsky, E. & Talipova, T. 2011 Nonlinear random wave field in shallow water: variable Korteweg–de Vries framework. Nat. Hazards Earth Syst. Sci. 11, 323–330.Google Scholar
Trulsen, K., Zeng, H. & Gramstad, O. 2012 Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys. Fluids 24, 097101.Google Scholar
Viotti, C. & Dias, F. 2014 Extreme waves induced by strong depth transitions: fully nonlinear results. Phys. Fluids 26, 051705.Google Scholar
Zeng, H. & Trulsen, K. 2012 Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom. Nat. Hazards Earth Syst. Sci. 12, 631–638.Google Scholar
Zhang, J., Benoit, M., Kimmoun, O., Chabchoub, A. & Hsu, H.-C. 2019 Statistics of extreme waves in coastal waters: large scale experiments and advanced numerical simulations. Fluids 4 (99), 1–24.Google Scholar