Multi-scale processes are ubiquitous in nature; from soil dynamics to biological processes (micro-organisms, plants, animals), and from crack formation in rocks (buildings, volcanos) to climate and turbulence and mixing and diffusion. All these phenomena, and many more, show processes occurring on different scales, and complex non-linear interactions between the different scales. Scaling is thus of fundamental importance in how such processes. How are observations at one scale related to those at another scale? How are such processes organized in space and time? How do such interactions scale across the different scales? What is the role of intermittency?


This course will include all aspects of scaling, nonlinearity, and complexity on geosciences using cross-disciplinary approaches involving fluid dynamics, mixing, and diffusion, and turbulence. Theoretical, numerical, experimental, and modeling approaches are appropriate. Methods of analysis, such as fractal/multifractals, spectral analysis, statistical scaling analysis, data mining, time series analysis, and more, are included. Research work on processes occurring at the laboratory, local, regional, continental, or global scales are all appropriate.

An example is the turbulence generated by the newly proposed sparse 3D multi-scale grids which has a reduced blockage ratio compared to the classical flat fractal grids. A key question is, can this enhance turbulent mixing efficiency? Another example, at the small scales, viscosity or surface tension is important, but at turbulent flows transport affect the dynamics of the ecosystem in a non-linear fashion, from the low (primary producers) to high (fish) trophic levels; finally, at the long geological scale, global oceanic and atmospheric circulation interact with the biological pump modulating the biogeochemical fluxes of essential elements.

In a cross-disciplinary context, a review of experimental data on non-linear elasticity of soils and sedimentation and percolation using multi-fractals is appropriate. Can we interpret the data using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio?