Evolution of solitons over a randomly rough seabed

Area of Science:

• Fluid dynamics
• Nonlinear wave phenomena
• Oceanography

Background:

• Long waves are crucial in oceanography and coastal engineering.
• Seabed topography significantly influences wave propagation.
• Existing models often simplify seabed complexity.

Purpose of the Study:

• To develop a modified Korteweg-de Vries (KdV) equation for long waves over randomly uneven seabeds.
• To incorporate the effects of seabed disorder on wave amplitude attenuation and phase.
• To analyze soliton behavior in disordered environments.

Main Methods:

• Derivation of a modified Korteweg-de Vries (KdV) equation.
• Analytical solutions for wave evolution.
• Numerical simulations of soliton dynamics.

Main Results:

• The modified KdV equation accurately describes amplitude attenuation and phase shifts due to seabed disorder.
• Solitons entering disordered regions experience modified evolution.
• Solitons passing over finite disordered regions can undergo fission, creating new solitons.

Conclusions:

• Seabed disorder introduces significant modifications to long wave propagation.
• The derived modified KdV equation provides a valuable tool for studying nonlinear waves in realistic oceanic conditions.
• Understanding soliton fission in disordered environments is key for predicting wave behavior.