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Technical Report2005 program of studies : fast times and fine scales(Woods Hole Oceanographic Institution, 2006-07) Buhler, Oliver ; Doering, Charles ; Keller, Joseph ; Papanicolaou, George C. ; Eijnden, Eric VandenThe 2005 GFD program was entitled “Fast Times and Fine Scales” with a focus on asymptotic and stochastic modeling methods that exploit a physical scale separation of some kind. An extremely strong application pool resulted in the appointment of the unusually large class of eleven GFD Fellows for the summer. The first week consisted of principal lectures from Joe Keller on waves in fluids, ray methods and a variety of applications. The second week was divided between Eric Vanden-Eijnden’s lectures on Brownian motion and stochastic diffferential equations, and George Papanicolaou’s lectures on variational principles and asymptotic methods in homogenization theory. The principal lectures were particularly well-attended but the lecture room at Walsh Cottage proved up to the task of accommodating the full audience. Research lectures by staff and visitors were delivered daily throughout the program addressing topics ranging from applications of multiscale modeling methods in ocean and atmosphere dynamics, to applications of stochastic methods in populations dynamics and chemical kinetics, to applications of homogenization theory in materials science and engineering. The program also included a popular public lecture on the timely subject of tsunamis. And as usual this summer ended with the Fellows’ reports including two experimental projects and theoretical work on a variety of problems inspired by the summer’s research theme. Oliver Bühler and Charlie Doering acted as co-Directors for the summer. Janet Fields, Jeanne Fleming and Penny Foster provided the administrative backbone for the program. Keith Bradley supplied technical support, and Matt Finn ran the computer network and graciously helped with the production of the summer’s proceedings volume. As always we are grateful to Woods Hole Oceanographic Institution for the use of Walsh Cottage, the perfect setting for the GFD program.
Technical Report2015 program of study : stochastic processes in atmospheric & oceanic dynamics(Woods Hole Oceanographic Institution, 2016-11) Wettlaufer, John ; Buhler, OliverStochastic 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.
PreprintWave–vortex decomposition of one-dimensional ship track data( 2014-07-29) Buhler, Oliver ; Callies, Joern ; Ferrari, RaffaeleWe present a simple two-step method by which one-dimensional spectra of horizontal velocity and buoyancy measured along a ship track can be decomposed into a wave component consisting of inertia–gravity waves and a vortex component consisting of a horizontal flow in geostrophic balance. The method requires certain assumptions for the data regarding stationarity, homogeneity, and horizontal isotropy. In the first step an exact Helmholtz decomposition of the horizontal velocity spectra into rotational and divergent components is performed and in the second step an energy equipartition property of hydrostatic inertia–gravity waves is exploited that allows diagnosing the wave energy spectrum solely from the observed horizontal velocities. The observed buoyancy spectrum can then be used to compute the residual vortex energy spectrum. Further wave–vortex decompositions of the observed fields are possible if additional information about the frequency content of the waves is available. We illustrate the method on two recent oceanic data sets from the North Pacific and the Gulf Stream. Notably, both steps in our new method might be of broader use in the theoretical and observational study of atmosphere and ocean fluid dynamics.
Technical Report2009 program of studies : nonlinear waves(Woods Hole Oceanographic Institution, 2010-01) Buhler, Oliver ; Helfrich, Karl R.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 wide-ranging lecture course, but not least due to the valiant efforts of Pascale Garaud, who coordinated the write-up and proof-read 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 one-hour lecture. As always, these projects are the heart of the research and education aspects of our summer study.