1991 Summer Study Program in Geophysical Fluid Dynamics : patterns in fluid flow

Funding was provided by the National Science Foundationthrough Grant No. OCE 8901012.

The GFD program in 1991 focused on pattern forming processes in physics and geophysics. The pricipallecturer, StephanFauve, discussed a variety of systems, including our old favorite, Rayleigh-Bénard convection, but passing on to exoticexamples such as vertically vibrated granular layers. Fauve's lectures emphasize a unified theoretical viewpoint based onsymmetry arguments. Patterns produced by instabilties can be described by amplitude equations, whose form can be deducedby symmetry arguments, rather than the asymptotic expansions that have been the staple of past Summer GFD Programs. Theamplitude equations are far simpler than the complete equations of motion, and symetry arguments are easier thanasymptotic expansions. Symmetry arguments also explain why diverse systems are often described by the same amplitudeequation. Even for granular layers, where there is not a universaly accepted continuum description, the appropnate amplitudeequation can often be found using symmetry arguments and then compared with experiment.Our second speaker, Daniel Rothan, surveyed the state of the art in lattice gas computations. His lectures illustrate thegreat utility of these methods in simulating the flow of complex multiphase fluids, particularly at low Reynolds numbers. Thelattice 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. Theyrange from the formation of sand dunes, though the theory of lattice gases, and on to two dimensional-turbulence andconvection on planetary scales. Readers desiring to quote from these report should seek the permission of the authors (apartial list of electronic mail addresses is included on page v). As in previous years, these reports are extensively reworked forpublication or appear as chapters in doctoral theses. The task of assembling the volume in 1991 was at first faciltated by ournewly acquired computers, only to be complicated by hurricane Bob which severed electric power to Walsh Cottage in thefinal hectic days of the Summer.