Extreme wave statistics in the surface elevation and the velocity field for waves propagating over a shoal
Abstract
It was previously shown that for irregular water surface waves evolving over a shoal the surface elevation field could experience a local maximum of kurtosis and skewness on top of the shoal, and a local minimum of skewness after the shoal. Raustøl (2014) showed experimentally that this behavior occurs when the depth is below a certain threshold, in qualitative agreement with earlier experimental results by Trulsen et al. (2012) and numerical results by Sergeeva et al. (2011), Zeng & Trulsen (2012), Gramstad et al. (2013) and Viotti & Dias (2014). In a new series of experiments we have also measured the horizontal velocity field in the water close to the equilibrium water surface. We have found that while the skewness of the velocity field behaves qualitatively similar to the skewness of the surface elevation field, the kurtosis of the velocity field behaves qualitatively different. The kurtosis of the velocity field does not achieve a local maximum on top of the shoal, and instead achieves a local maximum after the shoal. Acknowledgments This research has been supported by the Research Council of Norway through grant RCN 256466 ExWaMar. References [1] 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. [2] RAUSTØL, A. 2014 Freake bølger over variabelt dyp. Master's thesis, University of Oslo. [3] 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. [4] TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys. Fluids 24, 097101. [5] VIOTTI, C. & DIAS, F. 2014 Extreme waves induced by strong depth transitions: Fully nonlinear results. Phys. Fluids 26, 051705. [6] 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.
- Publication:
-
EGU General Assembly Conference Abstracts
- Pub Date:
- April 2019
- Bibcode:
- 2019EGUGA..21.5507T