Physics, Nonlinear Time Series Analysis, Data Assimilation and Hyperfast Modeling of Nonlinear Ocean Waves

摘要

My new book Nonlinear Ocean Waves and the Inverse Scattering Transform, (Osborne, 2010) discusses the physics, nonlinear time series analysis, data assimilation and hyperfast modeling of nonlinear ocean waves. Some of the material in this book consists of mathematics not always familiar to oceanographers and may require an investment of the reader's time to take full advantage of the methods introduced there. This book, in many ways, may be compared to the book Ocean Wave Spectra (ONR, 1962), which was published in a revolutionary time for the field of wind waves (the 1950s and 60s). New data analysis procedures were being developed by Pierson, Longuet-Higgins, Munk, Hasselmann and others. The concept of the power spectrum was quite new to physical oceanographers. It is useful in this context to recall the work of Paley, Weiner and Rice in the 1930s and 1940s and the subsequent application to power spectra and wind waves in the 1950s and 1960s: This work was based upon the integrable of the square root of dx. I recall well the consternation of physical oceanographers at that time about this seemingly impossibly difficult mathematics (see Kinsmann's book for aid in understanding what was at that time the new mathematics). Likewise the introduction of the Hasselmann equation in 1961 was based on the derivation of kinetic equations from the Euler equations, also rather esoteric mathematics at that time. Now of course these areas of mathematics have been absorbed into the mainstream of wind/wave research and have lead to the development of modern forecasting and hindcasting models. Indeed the mathematics of 1960 seems mainstream today.