Ergodicity and spectral cascades in point vortex flows on the sphere

A.C.P. was supported under DOD (MURI) Grant No. N000141110087 ONR. The computations were supported by the CUNY HPCC under NSF Grants No. CNS-0855217 and No. CNS-0958379.We present results for the equilibrium statistics and dynamic evolution of moderately large [n = O (102 - 103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k-1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.Publisher PDFPeer reviewe

Lagrangian velocity statistics of directed launch strategies in a Gulf of Mexico model

International audienceThe spatial dependence of Lagrangian displacement and velocity statistics is studied in the context of a data assimilating numerical model of the Gulf Mexico. In the active eddy region of the Western Gulf, a combination of Eulerian and Lagrangian measures are used to locate strongly hyperbolic regions of the flow. The statistics of the velocity field sampled by sets of drifters launched specifically in these hyperbolic regions are compared to those produced by randomly chosen launch sites. The results show that particle trajectories initialized in hyperbolic regions preferentially sample a broader range of Eulerian velocities than do members of ensembles of randomly launched drifters. The velocity density functions produced by the directed launches compare well with Eulerian velocity pdfs. Implications for the development of launch strategies to improve Eulerian velocity field reconstruction from drifter data are discussed

Synthesis of Di(s-triazinyl) Sulphides and Disulphides. The-Promoting Effect of Oxidants on the Cleavage of the Thioether Bond

Synthesis of a number of di(s-triazinyl) sulphides and disu1phides is described. The behaviour of these compounds on oxidative attack has been examined. It has been found that instead of the expected sulphoxide and/or sulphone formation upon oxidation, a simple scission of the thioether linkage takes place, yielding a hydroxytriazine and the corresponding disulphide

Synthesis of Di(s-triazinyl) Sulphides and Disulphides. The-Promoting Effect of Oxidants on the Cleavage of the Thioether Bond

Synthesis of a number of di(s-triazinyl) sulphides and disu1phides is described. The behaviour of these compounds on oxidative attack has been examined. It has been found that instead of the expected sulphoxide and/or sulphone formation upon oxidation, a simple scission of the thioether linkage takes place, yielding a hydroxytriazine and the corresponding disulphide

Death of three Loop Current rings

The life cycle of large anticyclonic rings in the Gulf of Mexico (GOM) is widely described by pinch off from the Loop Current, migration across the Gulf and eventual spin down along the western slope. Extensive observational and modeling efforts provide a relatively consistent picture of rings pinching off from the Loop Current and of complex interaction between anticyclones and cyclones driven by bathymetry along the western and northwestern shelf. The observational record for Loop Current rings (LCRs) during the intermediate period of westward translation is less clear. A number of studies recognize distinct anomalies in LCR characteristics in deep water as the rings enter the western Gulf near 92-94W. These include abrupt changes in the geometry of observed drifter trajectories and derived eddy parameter fits as well as changes in both ring translation speeds and the estimated rate of ring decay. Such observations are consistent with intense interaction and mass exchange between the rings and other coherent mesoscale features known to be present in the western Gulf. We test the hypothesis that interactions with the ambient mesoscale field can lead to rapid loss of coherence of some LCRs well before they reach the \u27eddy graveyard\u27 in the western Gulf. We use the data-assimilating, eddy-resolving numerical GOM model described by Kantha et al. (2005) to assess the fates of readily identified LCRs Fourchon, Juggernaut, and Millenium during the period July 1998 to August 2001. Lagrangian metrics, including relative dispersion of small drifter clusters seeded in the ring cores, analysis of evolving blobs seeded in the ring cores, and finite-scale Lyapunov exponents, are used to track model ring evolution. These metrics clearly show that interactions with existing mesoscale cyclones and anticyclones caused Fourchon and Juggernaut to break up near 92W on advective time scales. In addition, Millenium also experienced an intense deformation, stirring, and mixing episode near 92W. Blob studies showed that the core fluid of Millenium was ultimately dispersed over much of the western basin. Our results show that some LCRs may break up through interactions with existing western Gulf cyclones and anticyclones prior to reaching the western slope

Submesoscale Kinematic Properties in Summer and Winter Surface Flows in the Northern Gulf of Mexico

Statistical properties of near-surface horizontal velocity gradients are obtained from four drifter experiments conducted in the Gulf of Mexico during Summer 2012 and Winter 2016. The data density provided by the near-simultaneous deployments of 90-326 surface drifters in each allows direct, drifter-based estimates of the scale dependence of velocity gradients at separation scales ranging from 200 m to 5 km. The robustness of these estimates, derived from uniquley sampled, nearly equilateral triplets, is confirmed by comparisons with estimates produced from larger drifter clusters, and with estimates based on concurrent Eulerian X-band radar observations. The winter launches were deployed above a ∼80 m deep mixed layer, one in a region with nearly homogeneous horizontal density structure, the other in a region of strong surface density gradients associated with filaments of fresh Mississippi River water. The summer launches occurred in a shallow (10m) mixed layer, one launched across a mesoscale frontal jet separating regions of horizontally homogeneous density and the other, similar to the corresponding winter launch, also in a region filamented by shallow lenses of cold, fresh water. Seasonal differences are observed, with larger velocity fluctuations and greater variance in divergence and vorticity, especially at the smallest scales, in winter. Differences between same-season launches are, however, as large as seasonal differences. In both seasons, observations sampling regions directly impacted by fresh water fluxes show strongly skewed vorticity distributions, with cyclonic vorticity dominating strain. For the other launches, one in each season, strain dominated minimally skewed vorticity

Reconstructing Basin-Scale Eulerian Velocity Fields From Simulated Drifter Data

A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km x 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deployed in the 1000 km x 1400 km energetic western region. The base reconstruction error, achieved with full observation of the velocity field, ranges from 5% (with 191 basis functions) to 30% (with 65 basis functions). Specific analysis of the relation between spatial coverage and reconstruction error is presented using 180 drifters deployed in 100 different initial configurations that maximize coverage extremes. The simulated drifter data is projected on 107 basis functions for a 50-day period. The base reconstruction error of 15% is achieved when drifters occupy approximately 110 (out of 285) 70-km cells in the western region. Reconstructions from simulated mooring data located at the initial positions of representative good and poor coverage drifter deployments show the effect drifter dispersion has on data voids. The authors conclude that with appropriate coverage, drifter data could provide accurate basin-scale reconstruction of Eulerian velocity fields

Studies on Covalent Adducts of Dehydrouric Acid

The structure of 5-chloro and 5-alkoxy-5,7-dihydro-3//-purine-2,4,6-trio- nes (6 and 7-9) has been corroborated by their spectral properties and X-ray crystallography. The stereochemical model (fì)-10 of the key uricolytic intermediate was prepared using menthol as chiral auxiliary. In acidic solutions, depending on the N-substitution, the ring cleavage occurred either at the 4,9-bond 6b -» 13 (R1 = Me) or at the 3,4-bond 6c -» 14 (R1 = H). Opening of the 1,6-bond is the dominant process under alkaline conditions. Decarboxylative rearrangement into 1,3-dimethylallantoin (15) was specific for N(7)-unsubstituted derivatives. Evidence for intermediacy of the bicyclol tautomeric form was supplied by isolation of l-menthoxy-2,4-dimethyl-3,7-di- oxo-2,4,6,8-tetraazabicyclo[3.3.0]octane (16); fragmentation of 10 into 5- menthoxy-imidazolidin-2,4-dione (17) also takes place under forcing conditions. Conversely, no allantoin rearrangement was encountered in the R7*H cases; 7d underwent the pyrimidine ring fragmentation to give 5-methoxy-l- methyl-4-methylimino-imidazolidine-2-one (18) or 5-carboxamido-5-methoxy- l-methyl-4-methylimino-imidazolidine-2-one (19). A possible mechanism for these ring transformation reactions is discussed

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 meters to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. \textcolor{black} {Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200m$-$50km scales and clearly indicate that dispersion at the submesoscales is \textit{local}, driven predominantly by energetic submesoscale fluctuations.} The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.Comment: 9 pages, 6 figure

CHOICE OF PLANTS FOR ROOF GARDENS

Ograničena dubina supstrata, suša, vjetar, visoke temperature i slaba drenaža uvjeti su koje mogu podnijeti samo određene biljne vrste. Ovim radom se želi istaknuti one biljne vrste koje mogu uspijevati u specifičnim životnim uvjetima kakvi vladaju na krovu, a koje ujedno ispunjavaju kriterije održavanja te one estetske.A shallow growing medium, draught, wind, high temperatures and bad drainage are conditions in which only rare plant species can grow. The goal of this paper is to highlight and describe plant species that can survive and grow on roofs and match criteria of maintenance and aesthetics at the same time