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Local run-up amplification by resonant wave interactions
Themistoklis S Stefanakis1, Frédéric Dias, Denys Dutykh
1CMLA, ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan cedex, France.
Physical Review Letters
|October 27, 2011
Summary
This study reveals resonant regimes in long wave run-up, enhancing nonleading waves on beaches. These phenomena amplify run-up for both elevation and depression waves, impacting coastal dynamics.
Area of Science:
- Coastal Engineering
- Fluid Dynamics
- Oceanography
Background:
- Previous analyses of long wave run-up focused on maximum run-up values.
- The existence of resonant regimes and their impact on run-up were not fully captured.
Purpose of the Study:
- Investigate resonant phenomena in long wave run-up on plane and nontrivial beaches.
- Analyze the influence of resonant regimes on run-up amplification.
- Explore the energy evolution and effects of dispersion.
Main Methods:
- One-dimensional numerical simulations using nonlinear shallow water equations.
- Boundary value problem analysis for various beach slopes.
- Utilized monochromatic waves and simulated tsunami data as forcing conditions.
Main Results:
- Identified resonant phenomena between incident wavelength and beach slope.
- Observed enhanced run-up for nonleading waves, including both elevation and depression waves.
- Found a quasiperiodic state in energy evolution for sinusoidal waves.
- Dispersion slightly reduced maximum run-up but did not alter the overall behavior.
Conclusions:
- Resonant regimes significantly influence long wave run-up, leading to amplification.
- The study provides a more comprehensive understanding of wave dynamics on beaches.
- Findings are relevant for coastal hazard assessment and engineering designs.
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