Summer Study Program in Geophysical Fluid Dynamics 1991. Patterns in Fluid Flow

摘要

The GFD program in 1991 focused on pattern forming processes in physics andgeophysics. The principal an Fauve, discussed a variety of systems, including our old favorite, Rayleigh-Benard convection, but passing on to exotic examples such as vertically vibrated granular layers. Fauve's lectures emphasize a unified theoretical viewpoint based on symmetry arguments. Patterns produced by instabilities can be described by amplitude equations, whose form can be deduced by symmetry arguments, rather than the asymptotic expansions that have been the staple of past Summer GFD Programs. The amplitude equations are far simpler than the complete equations of motion, and symmetry arguments are easier than asymptotic expansions. Symmetry arguments also explain why diverse systems are often described by the same amplitude equation. Even for granular layers, where there is not a universally accepted continuum description, the appropriate amplitude equation can often be found using symmetry arguments and then compared with experiment. Our second speaker, Daniel Rothman, surveyed the state of the art in lattice gas computations. His lectures illustrate the great utility of these methods in simulating the flow of complex multiphase fluids, particularly at low Reynolds numbers. The lattice gas simulations reveal a complicated phenomenology much of which awaits analytic exploration. The fellowship lectures cover broad ground and reflect the interests of the staff members associated with the program. They range from the formation of sand dunes, through the theory of lattice gases, and on to two dimensional-turbulence and convection on planetary scales. Pattern formation, Convection, Dynamical system.