The vigorous stirring of a cup of tea gives rise, as we all know, to interesting fluid dynamical phenomena, some of which are very hard to explain. In this book our "cup of tea" contains the currents of the Earth's atmosphere, oceans, mantle, and fluid core. Our goal is to under stand the basic physical processes which are most important in describing what we observe, directly or indirectly, in these complex systems. While in many respects our understanding is measured by the ability to predict, the focus here will be on relatively simple models which can aid our physical intuition by suggesting useful mathematical methods of investiga tion. These elementary models can be viewed as part of a hierarchy of models of increasing complexity, moving toward those which might be use fully predictive. The discussion in this book will deal primarily with the Earth. Interplanetary probes of Venus, Mars, Jupiter and Saturn have revealed many exciting phenomena which bear on geophysical fluid dynamics. They have also enabled us to see the effect of changing the values of certain parameters, such as gravity and rotation rate, on geophysical flows. On the other hand, satellite observations of our own planet on a daily and hourly basis have turned it into a unique laboratory for the study of fluid motions on a scale never dreamt of before: the motion of cyclones can be observed via satellite just as wing tip vortices are studied in a wind tunnel.

This volume reflects the current state of scientific knowledge about natural climate variability on decade-to-century time scales. It covers a wide range of relevant subjects, including the characteristics of the atmosphere and ocean environments as well as the methods used to describe and analyze them, such as proxy data and numerical models. They clearly demonstrate the range, persistence, and magnitude of climate variability as represented by many different indicators. Not only do natural climate variations have important socioeconomic effects, but they must be better understood before possible anthropogenic effects (from greenhouse gas emissions, for instance) can be evaluated. A topical essay introduces each of the disciplines represented, providing the nonscientist with a perspective on the field and linking the papers to the larger issues in climate research. In its conclusions section, the book evaluates progress in the different areas and makes recommendations for the direction and conduct of future climate research. This book, while consisting of technical papers, is also accessible to the interested layperson.

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

The study of the magnetic fields of the Earth and Sun, as well as those of other planets, stars, and galaxies, has a long history and a rich and varied literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is therefore needed. Dynamo theory offers an explanation of natural magnetism as a phenomenon of magnetohydrodynamics (MHD), the dynamics governing the evolution and interaction of motions of an electrically conducting fluid and electromagnetic fields. A natural starting point for a dynamo theory assumes the fluid motion to be a given vector field, without regard for the origin of the forces which drive it. The resulting kinematic dynamo theory is, in the non-relativistic case, a linear advection-diffusion problem for the magnetic field. This kinematic theory, while far simpler than its magnetohydrodynamic counterpart, remains a formidable analytical problem since the interesting solutions lack the easiest symmetries. Much ofthe research has focused on the simplest acceptable flows and especially on cases where the smoothing effect of diffusion can be exploited. A close analog is the advection and diffusion of a scalar field by laminar flows, the diffusion being measured by an appropriate Peclet number. This work has succeeded in establishing dynamo action as an attractive candidate for astrophysical magnetism.

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.

Theories and opinions about climate change abound – from those claiming human-induced climate change is already beyond control to those who express scepticism about the real extent of these changes. How should we weigh up the scientific evidence, and what role does climate change play in the history of the Earth? In this comprehensive history of the climate and climate change, Antonello Provenzale explains how the planetary climate system works and how the climate has evolved over millions of years. Starting from the catastrophic events that marked the early history of the Earth, including seas of magma, global glaciations and mass extinctions, he demonstrates how the climate has fluctuated between hot and cold periods, with the Earth hot and lush with forests at certain times and almost entirely covered by a thick layer of ice at others. The mechanisms that determine the modifications of the climate are multiple and complex and include external factors, such as solar luminosity and variations in the Earth's orbit, as well as internal processes connecting the atmosphere, the oceans, the crust, the mantle and the biosphere, composed of living organisms. While the climate has fluctuated a great deal over the Earth’s long history, there are two features of our current situation that are a source of real concern. First, the rise in temperature of the last fifty years has been extremely fast, making it difficult for the environment to adapt to the new conditions. Second, the human population is much greater than it was in the past, and this population needs water, food, energy and shelter to survive and flourish. If temperatures continue to rise as they have in recent decades, ours will not be an easy world in which to live. To appreciate what is at stake, we need to understand how the climate works and how human activity is affecting it – not in order to save the planet, which will do just fine on its own and probably better without us, but to save ourselves.