Geophysical Fluid Dynamics Program (GFD)
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The GFD Program began in 1959 at the Woods Hole Oceanographic Institution with the aim of introducing a then relatively new topic in mathematical physics, geophysical fluid dynamics, to graduate students in physical sciences. It has been held each summer since and promotes an exchange of ideas among the many distinct fields that share a common interest in the nonlinear dynamics of rotating, stratified fluids. These fields include classical fluid dynamics, physical oceanography, meteorology, astrophysics, planetary atmospheres, geological fluid dynamics, hydromagnetics, and applied mathematics.
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Technical Report2018 program of studies: sustainable fluid dynamics(Woods Hole Oceanographic Institution, 20240209)The 2018 GFD Program theme was Sustainable Fluid Dynamics with Professor Andrew Woods of the University of Cambridge serving as principal lecturer. Andy showed the audience in the cottage and on the porch how to find similarity solutions everywhere, from deep in the earth to high in the atmosphere. He expanded on his lectures with the fellows during “Andy time”, and stayed on throughout the summer to participate in the traditional debates on the porch with participants old and new. Andy also contributed enthusiastically to the supervision of the fellows, particularly when there was an opportunity to squirt food dye into an experiment.

Technical Report2017 program of studies: iceocean interactions(Woods Hole Oceanographic Institution, 201811)The 2017 Geophysical Fluid Dynamics Summer Study Program theme was IceOcean Interactions. Three principal lecturers, Andrew Fowler (Oxford), Adrian Jenkins (British Antarctic Survey) and Fiamma Straneo (WHOI/Scripps Institution of Oceanography) were our expert guides for the first two weeks. Their captivating lectures covered topics ranging from the theoretical underpinnings of icesheet dynamics, to models and observations of iceocean interactions and highlatitude ocean circulation, to the role of the cryosphere in climate change. These icy topics did not end after the first two weeks. Several of the Fellows' projects related to iceocean dynamics and thermodynamics, and many visitors gave talks on these themes.

Technical Report2016 program of study : Fluidstructure interaction in the living environment(Woods Hole Oceanographic Institution, 201908)The 2016 GFD Program theme was fluidStructure Interaction in the Living Environment with Professors Mike Shelley of New York University and Anette ‘Peko’ Hosol of the Massachusetts Institute of Technology serving as principal lecturers. Together they introduced the audience in the cottage and on the porch to a fascinating mixture of topics ranging from swimming and swarming to cycling and sprinting, with Professor Jun Zhang of New York University interjecting some more traditional GFD (and art) part way through. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer’s GFD fellow. Following the principal lecture notes are the written reports of the follows’ own research projects.

Technical Report2015 program of study : stochastic processes in atmospheric & oceanic dynamics(Woods Hole Oceanographic Institution, 201611)Stochastic Processes in Atmospheric & Oceanic Dynamics was the theme at the 2015 GFD Program. Professors Charlie Doering (University of Michigan) and Henk Dijkstra (University of Utrecht) were the principal lecturers. Their lectures were collectively twopronged. The first prong was launched by Charlie, who laid down the mathematical foundations of random variables, stochastic processes and the nature and analysis of stochastic differential equations. In the second, Henk took us through the many places in the Atmosphere, Ocean and Climate system where the infrastructure from the first prong plays out. John Wettlaufer and Oliver Bühler were the stochastic co‐directors. In keeping with the theme, the Cottage was in constant motion with many visitors and long‐term staff members. Following the thematic principal lectures, the seminar room was busy all summer, with talks spanning an impressive range of topics that we are typically fortunate to experience in Walsh Cottage. Importantly, some of the newer staff ably jumped into the supervision of fellows projects ‒ directly or indirectly. The fellows pursued a rich range of projects and have produced a fine set of reports.

Technical Report2014 program to study : climate physics and dynamics(Woods Hole Oceanographic Institution, 201509)From the Preface: The 2014 Geophysical Fluid Dynamics Summer Study Program started on June 16th, with the topic of Climate Physics and Dynamics. The topic proved very timely and attracted an unprecedented number of applications from brilliant students. Professors Kerry Emanuel (MIT) and Geoff Vallis (Exeter) gave the principal lectures. They began with the simplest energy balance models and then included adjustment of the vertical profiles by convection (dry and moist). Kerry delved more deeply into convection and the processes found in "cloudpermitting" models, including island effects and the spontaneous formation of clusters surrounded by dry regions. Geoff discussed the largerscale dynamics of the atmosphere and oceans, including the transports by eddies and the thermohaline circulation.

Technical Report2013 program of study : buoyancydriven flows(Woods Hole Oceanographic Institution, 201405)The 2013 Geophysical Fluid Dynamics Summer Study Program theme was Buoyancy Driven Flows. Professor Paul Linden of the University of Cambridge was the principal lecturer. He ably introduced the topic from simple beginnings to sophisticated models and observations, guiding the audience in the cottage and on the porch through fundamental theory and applications. A number of topics from the lectures resurfaced in the fellows' projects. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer's GFD fellows. Following the principal lecture notes are the written reports of the fellows' own research projects.

Technical Report2012 program of study : coherent structures(Woods Hole Oceanographic Institution, 201311)The 2012 GFD Program theme was Coherent structures with Professors Jeffrey Weiss of the University of Colorado at Boulder and Edgar Knobloch of the University of California at Berkeley serving as principal lecturers. Together they introduced the audience in the cottage and on the porch to a fascinating mixture of models, mathematics and applications. Deep insights snaked through the whole summer, as the principal lecturers stayed on to participate in the traditional debates and contributed stoutly to the supervision of the fellows. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer's GFD fellows. Following the principal lecture notes are the written reports of the fellows' own research projects. In 2012, the Sears Public Lecture was delivered by Professor Howard Bluestein, of the University of Oklahoma on the topic of "Probing tornadoes with mobile doppler radars". The topic was particularly suitable for the summer's theme: a tornado is a special examples of a vortex, perhaps the mother of all coherent structures in fluid dynamics. Howie "Cb" showed how modern and innovative measurement techniques can yield valuable information about the formation and evolution of tornadoes, as well as truly amazing images.

Technical Report2011 program of study : shear turbulence : onset and structure(Woods Hole Oceanographic Institution, 201108)The theme for the Program in Geophysical Fluid Dynamics for the summer of 2011 was Shear Turbulence: onset and structure. Ten days of principal lectures by FabianWale e and Rich Kerswell began the summer, and a large number of seminars on this and a variety of other topics then continued through the eighth week. These lectures are presented in these Proceedings and form (we believe) the most complete, connected account of this subject) Eleven fellows from around the globe helped to record the principal lectures, and each carried out a project of his/her own, presented in seminar during the tenth and nal week. All these lectures and projects are also presented in this Proceedings volume. The further seminars presented throughout the summer by visitors and (in some cases) by GFD faculty are also listed here. The popular Sears Lecture was given by L. Mahadevan. The title was On growth and form: geometry, physics and biology. It was indeed popular, drawing a large and enthusiastic audience.

Technical Report2010 program of study : swirling and swimming in turbulence(Woods Hole Oceanographic Institution, 201106)Swirling and Swimming in Turbulence was the theme at the 2010 GFD Program. Professors Glenn Flierl (M.I.T.), Antonello Provenzale (ISACCNR, Turin) and JeanLuc Thiffeault (University of Wisconsin) were the principal lecturers. Together they navigated an elegant path through topics ranging from mixing protocols and efficiencies to ecological strategies, schooling and genetic development. The first ten chapters of this volume document these lectures, each prepared by pairs of this summer’s GFD fellows. Following on are the written reports of the fellows’ own research projects.

Technical Report2009 program of studies : nonlinear waves(Woods Hole Oceanographic Institution, 201001)The fiftieth year of the program was dedicated to Nonlinear Waves, a topic with many applications in geophysical fluid dynamics. The principal lectures were given jointly by Roger Grimshaw and Harvey Segur and between them they covered material drawn from fundamental theory, fluid experiments, asymptotics, and reaching all the way to detailed applications. These lectures set the scene for the rest of the summer, with subsequent daily lectures by staff and visitors on a wide range of topics in GFD. It was a challenge for the fellows and lecturers to provide a consistent set of lecture notes for such a wideranging lecture course, but not least due to the valiant efforts of Pascale Garaud, who coordinated the writeup and proofread all the notes, we are very pleased with the final outcome contained in these pages. This year’s group of eleven international GFD fellows was as diverse as one could get in terms of gender, origin, and race, but all were unified in their desire to apply their fundamental knowledge of fluid dynamics to challenging problems in the real world. Their projects covered a huge range of physical topics and at the end of the summer each student presented his or her work in a onehour lecture. As always, these projects are the heart of the research and education aspects of our summer study.

Technical Report1979 summer study program in geophysical fluid dynamics : the Woods Hole Oceanographic Institution : notes on polar oceanography(Woods Hole Oceanographic Institution, 197911)The emphasis in this year's GFD program has been somewhat different from the past. We have tried to expose a theoretically oriented audience to the new body of observations pertaining to the Arctic and Antarctic circulation. We have, however, not departed from our traditional goal of encouraging broad based inquiries into the field of Geophysical Fluid Dynamics. We would like to believe that the breadth of interest and enthusiasm exhibited in these reports will stimulate future work in Polar Oceanography and Fluid Dynamics.

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)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 1977 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 197712)The lectures by Marten Landahl, recorded in the first part of this report, served as the introduction to the study of turbulence which was the principal theme of the nineteenth summer program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution.

Technical ReportNotes on the 1975 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1975)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 ReportNotes on the 1974 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1974)This year the central topic was the general circulation of the oceans. Some of the basic ideas used in winddriven and thermohaline studies were presented in the introductory course of lectures and simple models that have guided our thinking in the development of the topic were discussed. As part of the introductory lectures Peter Niiler developed a model of the mixed layer, exploring the reasoning and the parameterization behind the theories of this important boundary region at the surface of the ocean. Dennis Moore gave a careful account of transient flows in equatorial regions and showed how dynamical conditions on the eastern and western boundaries are satisfied by a superposition of planetary, Kelvin and Yanai waves. Peter Rhines concluded the series with a discussion of topographically induced low frequency motions. At the request of the students Joseph B. Keller gave a lecture on "Solution of Partial Differential Equations by Ray Theory".

Technical ReportNotes on the 1970 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1970)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.

Technical ReportNotes on the 1972 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1972)The effect of gravity on fluids of varying density is of fundamental importance in natural flows. This subject formed the topic of concentration for the fourteenth summer program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. We had the good fortune to hear Stewart Turner lecture on stratified flows just after he had completed the manuscript for his book on the subject. Turner chose to emphasize nonlinear and turbulent aspects of stratified flows and, therefore, had to give up the deductive approach in favor of treatments based on dimensional analysis and similarity arguments. This summary of the many experimental studies of these flows increased our awareness of the fascinating variety of phenomena in which stratification plays so vital a role.

Technical ReportNotes on the 1971 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1971)A topic, such as planetary atmospheric dynamics, is necessarily a speculative one because of the extreme difficulty of obtaining detailed observations. A single datum is often responsible for several "theories". Andy Ingersoll was continually challenged during his attempts to present a coherent picture of a broad spectrum of observations and speculations about the atmospheres of the planets. He emerged somewhat battered but still intact. All of us felt rewarded by his efforts. The formal lectures were followed by a microsymposium on planetary atmospheres which included discussions of the latest observations, speculative theories and simple models of certain gross features.

Technical ReportNotes on the 1973 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1973)Nonlinear wave interactions formed the theme of the fifteenth summer program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. Owen Phillips was our principal lecturer on this subject, He chose to emphasize interactions among small numbers of discrete wave modes, including both internal and surface gravity waves in his discussions. His lectures provided a stimulating introduction to this important subject. Phillips' lectures were supplemented by a lecture by William Simmons on experiments with interacting internal waves, and a lecture by Carl Wunsch on internal waves in the ocean. Later in the summer, Wunsch gave us a lecture series on practical timeseries analysis.

Technical ReportNotes on the 1969 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution(Woods Hole Oceanographic Institution, 1969)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.