Understanding the effects of transport and mixing processes in fluid flows is at the heart of many problems of atmospheric, oceanic and geological sciences. These problems are not only of great scientific interest in their own right, but are also currently of enormous practical importance. Examples include the stratospheric ozone hole phenomenon at high latitudes in both hemispheres, possible mid- latitude ozone depletion in the Northern Hemisphere, long-range transport and chemical transformation of chemical pollutants in the troposphere, the North Atlantic thermohaline circulation and possible future changes in that circulation, with their implications for European and North American climate, the biogeochemical processes controlling absorption of CO2 into the oceans, the existence of geochemical reservoirs in the mantle of the Earth and the generation, evolution and scale distribution of heterogeneities and their possible role in mantle convection.
Mathematical models have an important role in atmospheric, oceanic and geological sciences. They provide at framework for quantitative interpretation of data and are the basis for quantitative prediction of future changes. Over the past decade activity in the fields of nonlinear mathematics and mathematical physics has lead to greatly improved theoretical understanding of transport and mixing. One advance, arising out of developments in nonlinear mathematics, has been the identification and investigation of the chaotic advection phenomenon. A second advance, arising in part from the application of methods of mathematical physics to the problem of turbulence, has been improved understanding of the spatial structure and statistics of passive tracer fields in turbulent flows.
The above developments have not yet been exploited to their full potential to improve understanding of atmospheric, oceanic and geological flows. Progress requires a two-way interaction between theoreticians on the one hand and scientists expert in the geophysical applications on the other.
The proposed summer school will bring together young scientists working on relevant mathematical topics and those working on geophysic.