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Long wave run-up on random beaches
Denys Dutykh1, Céline Labart, Dimitrios Mitsotakis
1Université de Savoie-CNRS Laboratoire de Mathématiques, LAMA - UMR 5127, Campus Scientifique, 73376 Le Bourget-du-Lac, France. Denys.Dutykh@univ-savoie.fr
Physical Review Letters
|November 24, 2011
Summary
This study quantifies how bottom roughness affects maximum wave run-up height using a novel stochastic model and Monte Carlo simulations. Results show roughness significantly impacts wave run-up predictions compared to smooth shore models.
Area of Science:
- Coastal Engineering
- Fluid Dynamics
- Applied Mathematics
Background:
- Estimating maximum wave run-up height is crucial for coastal protection.
- Existing models often simplify shorelines as smooth, neglecting natural roughness.
- Bottom rugosity effects are typically approximated with ad hoc friction terms.
Purpose of the Study:
- To investigate the impact of bottom roughness on maximum wave run-up height.
- To develop and apply a stochastic model for bottom irregularity.
- To compare model results with conventional approaches.
Main Methods:
- Development of a stochastic model for bottom irregularity.
- Quantification of roughness effects using Monte Carlo simulations.
- Discretization of nonlinear shallow water equations via finite volume schemes.
Main Results:
- The stochastic model effectively quantifies the influence of bottom rugosity.
- Significant differences in wave run-up predictions were observed compared to smooth-bottom models.
- Finite volume schemes provided accurate numerical solutions.
Conclusions:
- Bottom roughness is a critical factor influencing maximum wave run-up height.
- The proposed stochastic model offers a more realistic approach to wave run-up estimation.
- This research advances understanding for improved coastal engineering designs.
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