273 research outputs found
Singular Bohr-Sommerfeld Rules for 2D Integrable Systems
In this paper, we describe Bohr-Sommerfeld rules for semi-classical
completely integrable systems with 2 degrees of freedom with non degenerate
singularities (Morse-Bott singularities) under the assumption that the energy
level of the first Hamiltonian is non singular. The more singular case of {\it
focus-focus} singularities is studied in [Vu Ngoc San, CPAM 2000] and [Vu Ngoc
San, PhD 1998] The case of 1 degree of freedom has been studied in [Colin de
Verdiere-Parisse, CMP 1999] Our theory is applied to some famous examples: the
geodesics of the ellipsoid, the -resonance, and Schroedinger operators on
the sphere . A numerical test shows that the semiclassical Bohr-Sommerfeld
rules match very accurately the ``purely quantum'' computations.Comment: postscript, 61 pages, figures best seen in color. Preprint Institut
Fourie
Quasigeostrophic flows and turbulence in a rotating homogeneous fluid
Submitted in partial fulfillment of the requirements for the degree of Doctor of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August, 1977Stimulated by new evidence from both "in situ" oceanic observations
and results from numerical modelling, a laboratory study of quasigeostrophic
flow and turbulence in a rotating homogeneous fluid has been undertaken.
Two dimensional turbulence driven by a uniform distribution of sources and
sinks which oscillate in time, can be fairly well reproduced in this context.
Inertial time scales are about ten times smaller than Ekman spinup
time, and typical Reynolds numbers read 2000. The observations emphasize
the spectral tendency of the energy containing eddies. The case of
no topography is first discussed. In steadily forced turbulence, it is
observed that the energy containing scale is significantly larger than
the forcing scale. In the decaying stage the red cascade is observed and
rates of interaction are measured. Theoretical arguments for both behaviors
are presented; the former concerning the forced turbulence case is
believed to be new.
The forcing is next applied over various large scale topographies,
modelling the geophysical beta effect. The polar beta plane geometry preserves
the above spectral characteristics but at the same time introduces
anisotropy into the flow pattern. A broad westward mean flow develops in
the north and is surrounded by a belt of cyclones lying on its southward
side. The calculated second-order Eulerian mean flows induced by steadily
and uniformly forced Rossby waves in a long zonal channel, exhibit much of
the same momentum distribution in the inertial regime. In contrast, the
"sliced cylinder" geometry which possesses no closed geostrophic contours
drastically modifies the above picture. Both mean flow production and a
large scale tendency for the eddies are inhibited. The geographical distribution of the eddy intensities and scales is now wildly inhomogeneous.
The second aspect of this work is a study of the interaction of Rossby
waves with mean flows. A zonally traveling, forced wave is generated near
the southern boundary of a polar beta plane. Due to energy radiation in
the free interior and (or) potential vorticity mixing by the finite amplitude waves, a westward zonal flow develops. The effect of the mean flow
upon the forced steady waves is to weaken the anticyclones and intensify
the cyclones. Pressure time series reveal a growth of harmonics and
general spectral broadening as the waves travel freely inwards, suggesting
active nonlinear interactions. An experimental test of Rhines' (1977) potential
vorticity mixing theory is also presented at free latitudes. The decay
period when the driving is suppressed shows that a net transfer from the
waves to the mean flow kinetic energy occurs. Connection with hydrodynamic
stability theory is discussed.
Interaction of Rossby waves with an externally generated westward mean
flow allows one to make a controlled study of the critical layer problem.
For small amplitude waves, the mean flow is accelerated in the entire region
between the forcing and the critical latitude which acts as a wall for mean
wave momentum. In nonlinear runs the steady profile of the westward flow
indicates that an accelerating force is acting everywhere, revealing the
increasing transmission of wave momentum through the critical layer. At
the same time, pressure measurements near the critical point show considerable
fine structure developing over a long time scale.
The third part deals with steady isolated source-sink flows in the
sliced cylinder geometry. The response of the fluid to a meridionally
oriented steady dipole extends exclusively westward of the forcing. The
viscously balanced solutions are discussed and relevance to oceanic abyssal
circulation is emphasized. With strong driving, the combination of
a cyclone to the north and an anticyclone to the south is absolutely
stable although the reverse configuration is not. A connection with a
certain class of free, steady, isolated, inertial solutions developed
recently by Stern (1976) is made.The DGRST . (FRACE) and the Joint Program in Oceanography, Massachusetts
Institute of Technology and the Woods Hole Oceanographic
Institution offered a fellowship for the first two years. The National
Science Foundation under Grant OCE75-2l 674 and the Office of Naval
Research under Contract N00014-74-C0262-NR-083-004 supported this study
for the final two years
Lagrangian eddy statistics from surface drifters in the eastern North Atlantic
In 1976–1977, 16 surface drifters were seeded regularly in an area about 100 km in diameter, providing a good opportunity to study diffusion induced by the mesoscale eddies present in this part of the eastern North Atlantic. It is found herein that Taylor\u27s formula relating the diffusivity (rate of dispersion) of marked fluid parcels to the integral of the Lagrangian correlation function is accurate up to 30 days. The diffusivity, initially zero, reaches a plateau after about 10 days. The diffusivities associated with the time scale of the energy containing eddies (30 days) are 2.3 107 cm2/s and 1.7 107 cm2/s in the zonal and meridional direction respectively. This is small in view of the surface eddy kinetic energy of the order of 100 cm2/s2. Accordingly the Lagrangian integral time scales are as short as 2 days. After 30 days, the diffusivity decreases and the dispersion saturates. The Lagrangian eddy energy content is therefore weak at low frequencies in contrast with subsurface Eulerian energy content obtained in the same area. The center of gravity of the Lagrangian and Eulerian energy spectrum indicates time scales respectively of 12 and 26 days. At frequencies higher than 0.1 cpd the Lagrangian velocity spectrum falls off with a −2 slope. This may be an indication of a balance between the Lagrangian acceleration of water parcels and the essentially white noise wind stress computed from a nearby weathership. Eulerian spectra at greater depths which had a similar −2 slope in this band but a much reduced energy level suggest an oceanic response strongly trapped at the surface
Binary-swap volumetric rendering on the T3D
Journal ArticleThis paper presents a data distributed parallel raytraced volume rendering algorithm and its implementation on the CRI T3D. This algorithm distributes the data and the computational load to individual processing units to achieve fast and high-quality rendering of high-resolution data. The volume data, once distributed, is left intact. The processing nodes perform local raytracing of their subvolume concurrently. No communication between processing units is needed during this local ray-tracing process. A subimages is generated by each processing unit and the final image is obtained by compositing subimages in the proper order by the Binary-Swap algorithm. Performance of this algorithm on the T3D is presented and compared to an implementation on the CM-5
On the movements of the North Atlantic Subpolar Front in the preinstrumental past
Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 29 (2016): 1545-1571, doi:10.1175/JCLI-D-15-0509.1.Three sediment records of sea surface temperature (SST) are analyzed that originate from distant locations in the North Atlantic, have centennial-to-multicentennial resolution, are based on the same reconstruction method and chronological assumptions, and span the past 15 000 yr. Using recursive least squares techniques, an estimate of the time-dependent North Atlantic SST field over the last 15 kyr is sought that is consistent with both the SST records and a surface ocean circulation model, given estimates of their respective error (co)variances. Under the authors’ assumptions about data and model errors, it is found that the 10°C mixed layer isotherm, which approximately traces the modern Subpolar Front, would have moved by ~15° of latitude southward (northward) in the eastern North Atlantic at the onset (termination) of the Younger Dryas cold interval (YD), a result significant at the level of two standard deviations in the isotherm position. In contrast, meridional movements of the isotherm in the Newfoundland basin are estimated to be small and not significant. Thus, the isotherm would have pivoted twice around a region southeast of the Grand Banks, with a southwest–northeast orientation during the warm intervals of the Bølling–Allerød and the Holocene and a more zonal orientation and southerly position during the cold interval of the YD. This study provides an assessment of the significance of similar previous inferences and illustrates the potential of recursive least squares in paleoceanography.OM acknowledges
support from the U.S. National Science Foundation. CW
acknowledges support from the European Research
Council ERC Grant ACCLIMATE 339108.2016-08-1
Stirring and mixing of thermohaline anomalies
Data from the Tourbillon Experiment in the eastern North Atlantic indicate clearly the stirring of waters with contrasting thermohaline properties by a mesoscale eddy, and the ensuing mixture which occurred. The observed features are discussed in relation to a mixing scenario which considers the salinity distribution in the eastern N. Atlantic associated with the Mediterranean Water (MW) outflow through the Straits of Gibraltar to provide a large-scale context. A mesoscale eddy near the boundary of this water mass advected and deformed a blob of MW, sharpening thermohaline fronts so that double diffusive frontal intrusions developed. Double diffusion processes are invoked as the basic mixing mechanism between the contrasting waters, and following the model of Joyce the lateral mesoscale diffusivity across these fronts is estimated to be 4 m2 s−1. Estimates are made of the lateral fluxes to sub-eddy scales (\u3c20 km) by a number of essentially independent approaches, viz: (a) evaluating the changes in the temperature, salinity and potential vorticity of a particular patch of water, the successive positions of which are deduced from daily optimal streamfunction charts constructed from direct current measurements; (b) evaluating the rate of increase of salinity of the inner shell of the eddy which is attributed to mixing with the more saline outer shell, (c) considering the warm salty blob of MW which was drawn into the eddy circulation as a dye patch and determining its rate of spreading from the increase of its radially symmetrical variance. All of these approaches indicate downgradient mixing of temperature, salinity and potential vorticity anomalies with effective lateral diffusivity of the order of 102 m2 s−1. This is considered to be a shear-augmented diffusivity. Using a salinity flux deduced from the eddy heat fluxes computed from the 8-month moored current meter data together with the large-scale salinity gradient implies large-scale diffusivities of the order 5 × 102 m2 s−1; these summarize the averaged effect of many eddy events and can be used to parameterize lateral mesoscale eddy fluxes. It is shown that salt fluxes of the magnitude estimated are of the order required to balance the input of salt through the Straits of Gibraltar and maintain the large-scale salinity distribution in the eastern North Atlantic
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