ABSTRACT

Many growth processes that shape the human environment generate structures over a wide range of scales, e.g., trees, rivers, lightning bolts. Likewise, most geophysical f lows happen on a wide range of scales, e.g., winds in the atmosphere, currents in the oceans, seismic waves in the mantle. In general, both kinds of phenomena are governed by nonlinear dynamical laws that give rise to chaotic behavior, and it is thus very difficult to follow their evolution, let alone predict it. Only in the last few decades could the systems of nonlinear equations modeling environmental f luid f lows be solved, thanks to the development of numerical methods and the advent of supercomputers. Although the present computer performances still remain insufficient to simulate from first principles, i.e., by direct numerical simulation (DNS), many environmental f luid f lows, especially those which are turbulent, appropriate multiscale representations may contribute to the success of that ongoing enterprise. The goal of this review is to present three of them: fractals, self-similar random processes, and wavelets.