| Based on the fundamental equations of geophysical fluid dynamics and the consequence of vertical density stratification, this research applies travelling wave coordinate to the 3-D Boussinesq fluid to study the nonlinear permanent Wave. An autonomous system of ordinary differential equations in two variables is obtained as follows:
(For the equations please see the PDF file.)
Rigorous study of the mathematical mechanics of the geometric topological structures in phase plane led to the conclusion that nonlinear wave is periodic in propagation direction and that solitary waves do not exist.
Further researches showed the travelling wave system can be transformed into a simpler form by using the Hamilton function and “action-angle” variables so that the complex nonlinear wave was simplified into a system like simple harmonic vibration.
Using the transformed form of nonlinear wave and the directional angle of travelling wave, the analytic solution of nonlinear inertia-gravity internal wave can be Written in the form
(For the equations please see the PDF file.) |
