What have I discovered from ocean phenomena

Abstract

Almost everything I have done in the last twenty years is based on what I have discovered from studying ocean phenomena. Specifically, the waves on the surface of the ocean and their dynamics. Two items stand out: The first one is from studying the evolution of the waves from ripples to fully developed giant ocean waves. To quantify the changes, I found that frequency is very different from what had been defined traditionally through Fourier analysis. Ture frequency should be determined by differentiation of the phase function defined by an adaptive method rather than by any form of integral transform. Therefore, it should have ever changing instantaneous values. The second discovery is from studying wave turbulence interactions. To reveal the detailed dynamics, I found that spectral representation should not be a single line on the frequency and energy plane. True spectrum should be a high dimensional manifold to cover all the possible dynamic interactions: additive and multiplicative ones. These discoveries have enabled me to develop a set of nonlinear and nonstationary data analysis tools to study many other phenomena, from turbulence to brain waves. They have led me to new wonders I have never even contemplated before.