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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
PubMed
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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.

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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.