The wavelet transform is applied to the analysis of transient waves propagating in a dispersive medium. The wavelet transform of the acceleration process of the transient flexural vibrations of an impact excited uniform beam resulted in a time-scale representation which provided a clear exposition of the time evolution of the spectral components during the dispersion process. Based on the examples, the advantanges and shortcomings of the wavelet transform are discussed. The global balance requirements for angular momentum, water and energy are discussed and the history of GFDL studies on these topics is reviewed.
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems.
The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. A Lagrangian form of the KdV equation is given which governs the evolution of nonlinear shallow water waves. Wave motion described by this equation in the context of the inverse scattering transform is discussed. Ostrovsky, L. A., and Yu.