Turbulence and Climate Dynamics

This book presents a modern view on turbulence and climate dynamics. The first part gives a brief description of the theory of fully developed turbulence. Understanding turbulence involves many aspects of modern physics. The connection to the theories of scaling, chaos and statistical mechanics is described through examination of so-called shell models. Shell models are systems of nonlinear ordinary differential equations with solutions that exhibit chaotic cascade behavior. In many respects the models resemble the spectral Navier-Stokes equation of turbulence, but they are computationally managable. Differences between turbulence in two and three dimensions are explained. These differences show up in the behavior and the predictability of the atmospheric flow. The second part gives an introduction to the theory of climate , times series analysis and stochastic dynamics theory. The climate variations observed in paleoclimatic records are analysed using state-of-the-art time series analysis. The analysis of ice core records indicates that the turbulent and chaotic nature of the climate system manifests itself in fundamental limitations in our ability to predict the future climate changes. This claim is supported on surprisingly good fits between ice core records and solutions of stochastic differential equations. These solutions allow the occurrence of unpredictable almost instantaneous big climatic jumps.