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Surface gravity waves over a two-dimensional random seabed.
Jørgen H Pihl1, Chiang C Mei, Matthew J Hancock
1Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. jh@pihl.as
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
Homogenization theory reveals how random sea bathymetry affects weakly nonlinear waves. A modified nonlinear Schrödinger equation predicts wave evolution, incorporating random effects for better forecasting.
Area of Science:
- Fluid dynamics
- Wave propagation
- Statistical mechanics
Background:
- Understanding wave behavior in random environments is crucial for coastal engineering and maritime safety.
- Previous models often simplified bathymetry, limiting accuracy for complex sea conditions.
Purpose of the Study:
- To develop a theoretical framework for analyzing weakly nonlinear wave evolution over random bathymetry.
- To derive and analyze a modified nonlinear Schrödinger equation that accounts for bathymetric randomness.
Main Methods:
- Extension of homogenization theory to random media.
- Derivation of a deterministic nonlinear Schrödinger equation for wave envelopes.
- Analytical and numerical investigation of wave diffraction and nonlinear effects.
Main Results:
- A linear term with a complex coefficient, dependent on bathymetry statistics, was introduced into the governing equation.
- Numerical simulations demonstrated the impact of random bathymetry height and plan form on wave diffraction.
- Nonlinearity effects were analyzed in conjunction with random bathymetry influences.
Conclusions:
- The derived model accurately captures the influence of random bathymetry on weakly nonlinear waves.
- The study provides a robust method for predicting wave behavior in complex, real-world sea conditions.
- Findings are applicable to improving coastal protection designs and maritime navigation safety.