EGU22-8285
https://doi.org/10.5194/egusphere-egu22-8285
EGU General Assembly 2022
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Extreme waves on vertically sheared flows: Statistical analysis of weakly nonlinear waves

Zibo Zheng, Yan Li, and Simen Ellingsen
Zibo Zheng et al.
  • Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway (zibo.zheng@ntnu.no)

A depth-dependent shear current can play a significant role in modifying the statistics of wave surface elevation, including the probability of rogue waves. This work develops a second-order theory in wave steepness for the prediction of a train of weakly nonlinear irregular waves, which extends Dalzell (1999) to allow for the influence of a depth-dependent background flow and does not rely on the assumption of irrotational flows.

The theory was implemented numerically and we focus on the analysis of statistical proprieties of random waves. The linear dispersion relation of the coupled wave-current system is solved implicitly by a direct integration method (Li & Ellingsen 2019).

Both a JONSWAP spectrum and a directionally spread distribution are used to generate random linear waves, to which second-order modifications are obtained in the presence and absence of a depth-dependent shear current. The resulting probability distributions of wave crest are found to be greatly different from the Tayfun distribution (Tayfun 1980). The shear current with positive or negative vorticity leads to an increase or decrease in the probability of rogue waves, respectively. We also analyse the effects of different shear current profiles on the wave group averaged from a number of largest waves, the spectral change, and skewness and kurtosis of wave elevation.

Key words: waves/free-surface flow, ocean surface waves, wave-current interaction

 

References

Dalzell, J. F. (1999) "A note on finite depth second-order wave–wave interactions." Applied Ocean Research 21 105-111.

Li, Y. and Ellingsen, S. Å. (2019) "A framework for modeling linear surface waves on shear currents in slowly varying waters." Journal of Geophysical Research: Oceans 124 2527-2545.  

Tayfun, M. (1980) "Narrow-band nonlinear sea waves. " Journal of Geophysical Research 85 1548-1552..

How to cite: Zheng, Z., Li, Y., and Ellingsen, S.: Extreme waves on vertically sheared flows: Statistical analysis of weakly nonlinear waves, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8285, https://doi.org/10.5194/egusphere-egu22-8285, 2022.

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