Meacham Stephen P.

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Meacham
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Stephen P.
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Technical Report

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

1991-09 , Young, Bill , Fauve, Stephan , DeRemer, Barbara Ewing , Meacham, Stephen P.

The GFD program in 1991 focused on pattern forming processes in physics and geophysics. The pricipallecturer, Stephan Fauve, discussed a variety of systems, including our old favorite, Rayleigh-Bénard 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 instabilties 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 symetry 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 universaly accepted continuum description, the appropnate amplitude equation 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 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, though the theory of lattice gases, and on to two dimensional-turbulence and convection on planetary scales. Readers desiring to quote from these report should seek the permission of the authors (a partial list of electronic mail addresses is included on page v). As in previous years, these reports are extensively reworked for publication or appear as chapters in doctoral theses. The task of assembling the volume in 1991 was at first faciltated by our newly acquired computers, only to be complicated by hurricane Bob which severed electric power to Walsh Cottage in the final hectic days of the Summer.

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Technical Report

Double-diffusive processes : 1996 Summer Study Program in Geophysical Fluid Dynamics

1997-07 , Meacham, Stephen P. , Tucholke, Dacia

The physics of double diffusion and the role that it plays in the ocean provided the central theme for the 1996 summer program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. Lectures and seminars given by staff and visitors surveyed observations, laboratory experiments and theoretical models of double diffusive phenomena. Several lectures dealt with the related phenomena of thermal convection in layered media, the dynamics of binary fluids, viscoelastic convection and magnetoconvection. Research projects by the fellows included experiments with double diffusion in a slot, work on the formation and evolution of staircases, double diffusion in stars and the interaction between convection and radiation. This volume includes write-ups of the principal lectures, report of the fellows' research projects and abstracts of some of the seminars. A list of presentations and a bibliography may be found at the back of the volume.

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Thesis

Baroclinic instability of a meridionally varying basic state

1984-06 , Meacham, Stephen P.

Several problems are addressed herein. They are loosely connected by the theme of resonant triad interactions. The main topic is the finite amplitude evolution of weakly unstable, linear eigenmodes in a meridionally varying version of Phillips' two-layer model. It is shown in chapter four that interactions between neutral modes and the unstable mode strongly influence the evolution of the latter and are capable of stabilising it before significant changes occur in the zonally averaged flow. The evolution of the unstable wave in the absence of such resonant triad effects is also considered and it is shown by example that the combined influence of changes to the mean flow and higher harmonics of the unstable wave is sufficient to equilibrate the unstable wave. (The higher harmonics are unimportant in the meridionally uniform version of this model). The enhanced importance of neutral sidebands and the details of the evolution are interpreted as being consequences of the structure of the eigenmodes of the linear problem. It is shown in chapter three that, near minimum critical shear, meridional variation of the potential vorticity gradient of the basic flow can introduce dramatic changes in the structure of the normal modes. Some aspects of resonant triad dynamics in a meridionally uniform, vertically sheared, two-layer model are considered in chapter two. It is shown that non-linear interactions between a resonant triplet of neutral waves can lead to baroclinic instability. It is also demonstrated that resonant interactions between a slightly supercritical unstable linear mode and two neutral waves can destabilise the weakly finite amplitude equilibration of the unstable mode that would occur in the absence of the sidebands. This demonstration is limited to the case in which the basic state is not close to minimum critical shear. Finally, the work of Loesch (1974) , who examined the evolution of a weakly unstable mode and a pair of neutral waves in a basic flow that is close to minimum critical shear, is repeated with the difference that critical layer effects are included.

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