Malkus
Willem V. R.
Malkus
Willem V. R.
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Technical ReportNotes on the 1964 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1964) Malkus, Willem V. R. ; Thayer, Mary C.Two distinctive features of largescale geophysical flows are that they are dominated by the earth's rotation and that they are turbulent. This year's lecture program was an exploration of recent achievements in the study of, first, the simplest examples of turbulence, and second, the rotational constraint.

Technical ReportOrder and disorder in planetary dynamos : summer study program in geophysical fluid dynamics(Woods Hole Oceanographic Institution, 198805) Malkus, Willem V. R. ; Berry, Mary EvansOur principal lecturer, Stephen Childress, can be seen emerging from the "magnetic cottage" he constructed to edify those of us who attended G.F.D. '87. His central theme was the kinematic properties of the "fast" dynamo, one whose growth rate is insensitive to electrical conductivity. These novel studies, and the seminars given by Andrew Soward and others, offer assurance of more mechanistic understanding of evolving magnetic fields in stars and planets. The timely juxtaposition of Childress' lectures on kinematic fast dynamos and the seminars by Bruce Bayly on inertial threedimensional instabilities of shear flow, may lead soon to a dynamic fastfast dynamo. Faster than convecting continents, slower than Antarctic bottom water, waves in the Earth's magnetic field move to the west. Geophysicists' knowledge of the underlying process appears to advance at a similar pace. Yet the dynamos of the summer season already have suggested hydromagnetic flows which offer hope both of realizeable laboratory dynamos and more realistic planetary models. Perhaps the pace of testable predictions will quicken?

Technical ReportNotes on the 1975 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1975) Malkus, Willem V. R. ; Thayer, Mary C.The central topic of this seventeenth Geophysical Fluid Dynamics program was fluid motion in the earth's mantle and core. Our principal lecturer, Dan McKenzie, first addressed himself to the task of separating solid behavior of the mantle from fluid behavior. When the level of protest diminished Dan advanced to his numerical studies of mantle convection. The relationship of these numerical experiments and geophysical observables was impressive indeed for this first generation of mantle modeling. Intertwined seminars from P. Molnar, B. Parsons, J. Sclater and T. Atwater exposed us to data gathering and its rationale at the frontiers of geophysics. The fluid properties of the core may be less suspect than those of the mantle, but how and why the core fluid moves is still a mystery. Our associate principal lecturer, Fritz Busse, discussed the geomagnetic evidence for core motion. Then moving quickly to the more abstract problems of model geodynamos, Fritz described in five lectures his achievement of a first complete dynamic dynamo driven by convection.

Technical ReportThe 1959 Summer Program of Theoretical Studies in Geophysical Fluid Dynamics(Woods Hole Oceanographic Institution, 195910) Malkus, Willem V. R.This tenweek workstudydiscussion program is centered about a formal course called Geophysical Fluid Dynamics. Eight participants are selected from graduate and postgraduate applicants. In the discussions emphasis is placed on the formulation of tractable research problems in geophysics. The participants are encouraged to work on satisfactory problems thus formulated and to continue with their research after returning to their respective institutions.

Technical ReportSummer study program in geophysical fluid dynamics : dynamic differentation(Woods Hole Oceanographic Institution, 198411) Malkus, Willem V. R. ; Mellor, Florence K.Those attending G.F.D. 1984 were introduced to the novel topic of Geological Fluid Mechanics by our Principal Lecturer, Herbert Huppert. He presented his studies both as a discipline with recent fascinating successes, and as a challenge to his listeners to further isolate mathematically tractable examples of these multicomponent flows. Geological Fluid Mechanics has been the responsible process for the formation and modification of most of the geological objects studied today. The dynamics of fluid mixtures in magma chambers, the changing fluid boundary conditions and composition during selective crystallization of parts of the melt, and the separation of fluid fractions of different density and viscosity all represent areas in which quantitative theories are currently being tested. However, equally many areas, including convection mechanisms in the Earth's core and quantitative predictions for upper mantle motion, resist simplistic modeling.

Technical ReportNotes on the 1969 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1969) Malkus, Willem V. R. ; Thayer, Mary C.The principal theme of this eleventh Summer Program has been Astrophysical Fluid Dynamics. As in the past, we have explored the region of overlap in technique and theory of our summer theme and other aspects of Fluid Dynamics. An interesting example of this overlap is the application of the physics of saltfinger instability, a significant oceanographic process, to instabilities due to differential rotation in the sun, a critical problem in stellar evolution.

Technical ReportGeophysical fluid dynamics : notes on the 1961 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1961) Malkus, Willem V. R.

Technical ReportNotes on the 1978 summer study program on dynamo models of geomagnetism in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 197811) Malkus, Willem V. R. ; Thayer, Mary C.This was the twentieth Geophysical Fluid Dynamics program at Woods Hole. Stephen Childress of the Courant Institute was our principal lecturer. Dynamo theory, with all its interdisciplinary facets was our central theme. Geomagnetism and the solar magnetic cycle were brought closer to comprehension, yet none claimed a detailed predictive theory was near at hand. Perhaps J. Keller's lecture, entitled "Smooth equations for rough problems", best characterized the nature of these studies. Even then, the smooth equations are quite nonlinear, with Finiteamplitude magnetic solutions yet to be explored. Lectures intertwined with those of Childress exposed us to topics beside and outside his emphasis on a convective geodynamo.

Technical ReportNotes on the 1965 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1965) Malkus, Willem V. R. ; Thayer, Mary C.

Technical ReportThe 1960 Summer Program of Theoretical Studies in Geophysical Fluid Dynamics(Woods Hole Oceanographic Institution, 196011) Malkus, Willem V. R.This tenweek workstudydiscussion program is centered about a formal course called Geophysical Fluid Dynamics. Eight participants are selected from graduate and postgraduate applicants. In the discussions emphasis is placed on the formulation of tractable research problems in geophysics. The participants are encouraged to work on satisfactory problems thus formulated and to continue with their research after returning to their respective institutions.

Technical ReportNotes on the 1966 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1966) Malkus, Willem V. R. ; Thayer, Mary C.The lecturers, Drs. Howard, Stern and Veronis, have introduced the participants to several aspects of geophysical fluid dynamics at the frontiers of current research. Their choice of topic and its development was to serve, on one hand, a pedagogic function and, on the other, to suggest a variety of allied unsolved problems.

Technical Report1981 summer study program in geophysical fluid dynamics : physics of convection(Woods Hole Oceanographic Institution, 198111) Malkus, Willem V. R. ; Mellor, Florence K.Reexploring convection and its various transitions to chaotic behavior were the central themes of GFD 1981. Our principal lecturer, Dr. Edward A. Spiegel, provided both a rich historical picture and stimulating hours at the current frontiers of this topic. Before the summer was out his research lecture on "A Tale of Two Methods" elegantly merged Pierre Coullet's canonical formalism for studying dynamical systems in a central manifold and the more traditional twotiming amplitude expansions near critical points. Other lecture sequences on convection and its relation to simpler dynamical systems ranged from the fine presentations of John Guckenheimer on bifurcation theory to Fritz Busse's survey of his immense contributions to our understanding of nonlinear convection. The list of other lectures found on the following pages attests to our summerlong exposure to convection in the ocean, the atmosphere, the earth's core and mantle, and in the sun. August brought lectures on new observations of convection in the laboratories of physicists. Albert Libchaber's precise experiments on the many routes convection can take to turbulence, with parallel laboratory and numerical experiments described by J. Gollub and E. Siggia, added much to our language of inquiry.

Technical ReportNotes on the 1970 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1970) Malkus, Willem V. R. ; Thayer, Mary C.The principal lectures of this twelfth Summer Program were given by Joseph Pedlosky of the University of Chicago. On the following page one sees Dr. Pedlosky demonstrating advanced effects caused by rotation and stratification. Only in his last few lectures do these novel phenomena emerge from the analysis.