Non-Linear Modelling of Internal Geophysical Waves

Geophysical waves are waves that are found naturally in the Earth’s atmosphere and oceans. Internal waves, that act as an interface between fluids of different density are examples of geophysical waves. The system set-up will incorporate a model with a flat bottom, flat surface and internal wave. The system has a depthdependent current which mimics a typical ocean set-up and, as it is based on the surface of the rotating Earth, includes Coriolis forces. Using well established fluid dynamic techniques, the total energy is calculated and used to determine the dynamics of the system using a procedure called the Hamiltonian approach. By tuning a system variable several special cases such as irrotational or current-free are easily recovered. An approximate model utilising a small amplitude, long-wave regime, the so called Intermediate Long Wave (ILW) model is then derived using perturbation expansion techniques. Solutions are obtained that model waves that move without change of form called solitary waves. These waves can be referred to as solitons when their particle-like behaviour is considered. The Coriolis effect on the internal wave propagation is also examined following the idea of “nearly” Hamiltonian approach, developed in series of papers like [14, 15, 20, 48] and generalising the Hamiltonian approach of Zakharov [88]. The presented models have applications for climatologists, meteorologists, oceanographers, marine engineers, marine biologists and applied mathematicians