Nonlinear Dynamics of Random Surface Gravity Waves Over Water of Slowly Varying Depth |
| A. Perelomova
Gdansk University of Technology, Faculty of Applied Physics and Mathematics, 11/12 Gabriela Narutowicza Street, 80-233 Gdańsk, Poland |
| Full Text PDF |
| The weakly nonlinear propagation of a random surface wave over a water region of varying depth h is considered. A random, stationary Gaussian process describing perturbations in the volume of the liquid is assumed at infinite depth. The characteristics of the nonlinear random wave are evaluated as the wave propagates into shallow coastal waters. It is found that the mean amplitude of the fundamental harmonic of the wave is proportional to h7/8, while its variance is proportional to h7/4 as the wave approaches the coastal zone. The mean amplitude of the second harmonic is proportional to h-1/4. Manifestation of nonlinear effects becomes abrupt when the water depth falls below a certain critical value. This behavior occurs for relatively small energy densities of the perturbation at infinite depth, as specified in the study. For larger energy densities, nonlinear effects increase gradually. |
DOI:10.12693/APhysPolA.149.97 topics: dispersive media, nonlinear dynamics, surface gravity waves, random Gaussian process |