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Long Time-scales (long + time-scale)
Selected AbstractsGeneral Gyrokinetic Equations for Edge PlasmasCONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-9 2006H. Qin Abstract During the pedestal cycle of H-mode edge plasmas in tokamak experiments, large-amplitude pedestal build-up and destruction coexist with small-amplitude drift wave turbulence. The pedestal dynamics simultaneously includes fast time-scale electromagnetic instabilities, long time-scale turbulence-induced transport processes, and more interestingly the interaction between them. To numerically simulate the pedestal dynamics from first principles, it is desirable to develop an effective algorithm based on the gyrokinetic theory. However, existing gyrokinetic theories cannot treat fully nonlinear electromagnetic perturbations with multi-scale-length structures in spacetime, and therefore do not apply to edge plasmas. A set of generalized gyrokinetic equations valid for the edge plasmas has been derived. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. It turns out that the most general gyrokinetic theory can be geometrically formulated. The Poincaré-Cartan-Einstein 1-form on the 7D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincaré-Cartan-Einstein 1-form. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. As an example, the pullback transformation in the gyrokinetic Poisson equation is explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations. The familiar "polarization drift density" in the gyrocenter Poisson equation is replaced by a more general expression. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Numerical solution of the free-surface viscous flow on a horizontal rotating elliptical cylinderNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2008Roland Hunt Abstract The numerical solution of the free-surface fluid flow on a rotating elliptical cylinder is presented. Up to the present, research has concentrated on the circular cylinder for which steady solutions are the main interest. However, for noncircular cylinders, such as the ellipse, steady solutions are no longer possible, but there will be periodic solutions in which the solution is repeated after one full revolution of the cylinder. It is this new aspect that makes the investigation of noncircular cylinders novel. Here we consider both the time-dependent and periodic solutions for zero Reynolds number fluid flow. The numerical solution is expedited by first mapping the fluid film domain onto a rectangle such that the position of the free-surface is determined as part of the solution. For the time-dependent case a simple time-marching method of lines approach is adopted. For the periodic solution the discretised nonlinear equations have to be solved simultaneously over a time period. The resulting large system of equations is solved using Newton's method in which the form of the Jacobian enables a straightforward decomposition to be implemented, which makes matrix inversion manageable. In the periodic case all derivatives have been approximated pseudospectrally with the time derivative approximated by a differentiation matrix which has been specially derived so that the weight of fluid is algebraically conserved. Of interest is the solution for which the weight of fluid is at its maximum possible value, and this has been obtained by increasing the weight until a consistency break-down occurs. Time-dependent solutions do not produce the periodic solution after a long time-scale but have protuberances which are constantly appearing and disappearing. Periodic solutions exhibit spectral accuracy solutions and maximum supportable weight solutions have been obtained for ranges of eccentricity and angular velocity. The maximum weights are less than and approximately proportional to those obtained for the circular case. The shapes of maximum weight solutions is distinctly different from sub-maximum weight solutions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] Determining long time-scale hyporheic zone flow paths in Antarctic streamsHYDROLOGICAL PROCESSES, Issue 9 2003Michael N. Gooseff Abstract In the McMurdo Dry Valleys of Antarctica, glaciers are the source of meltwater during the austral summer, and the streams and adjacent hyporheic zones constitute the entire physical watershed; there are no hillslope processes in these systems. Hyporheic zones can extend several metres from each side of the stream, and are up to 70 cm deep, corresponding to a lateral cross-section as large as 12 m2, and water resides in the subsurface year around. In this study, we differentiate between the near-stream hyporheic zone, which can be characterized with stream tracer experiments, and the extended hyporheic zone, which has a longer time-scale of exchange. We sampled stream water from Green Creek and from the adjacent saturated alluvium for stable isotopes of D and 18O to assess the significance and extent of stream-water exchange between the streams and extended hyporheic zones over long time-scales (days to weeks). Our results show that water residing in the extended hyporheic zone is much more isotopically enriched (up to 11, D and 2·2, 18O) than stream water. This result suggests a long residence time within the extended hyporheic zone, during which fractionation has occurred owing to summer evaporation and winter sublimation of hyporheic water. We found less enriched water in the extended hyporheic zone later in the flow season, suggesting that stream water may be exchanged into and out of this zone, on the time-scale of weeks to months. The transient storage model OTIS was used to characterize the exchange of stream water with the extended hyporheic zone. Model results yield exchange rates (,) generally an order magnitude lower (10,5 s,1) than those determined using stream-tracer techniques on the same stream. In light of previous studies in these streams, these results suggest that the hyporheic zones in Antarctic streams have near-stream zones of rapid stream-water exchange, where ,fast' biogeochemical reactions may influence water chemistry, and extended hyporheic zones, in which slower biogeochemical reaction rates may affect stream-water chemistry at longer time-scales. Copyright © 2003 John Wiley & Sons, Ltd. [source] Observations of atmosphere-ocean coupling in the North AtlanticTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 576 2001Arnaud Czaja Abstract Anindex of sea surface temperature (SST) variability, ,T, is introduced that measures the difference in SST across the separated Gulf Stream in late winter. By analysing a long observational record of SST and sea-level pressure (SLP), it is shown that ,T exhibits damped oscillations of decadal period, and covaries with the strength of a dipolar SLP anomaly reminiscent of the North Atlantic Oscillation (NAO). Analysis in the frequency domain shows a broad-band ,peak' at 10,20 years in ,T, with a continuous decrease of power on longer time-scales. Similar spectral signatures are found in the northern part of the SLP dipole (the Greenland-Icelandic Low region) but not in its southern part (the subtropical High region), whose power increases on long time-scales. The observations are interpreted in the framework of a delayed-oscillator model in which the ocean circulation introduces the delay, and modulates ,T on decadal time-scales. The decrease of power seen on long time-scales (>25 years) in the ,T index is captured by a model including wind-driven ocean circulation, and arises primarily as a passive response of the latter to the NAO forcing. Variability of the ocean's meridional overturning circulation could also play a role in modulating ,T on decadal time-scales. If a small feedback of ,T on the NAO pattern is introduced, the simple model can also reproduce the spectral structures seen in the SLP anomaly in the Greenland-Iceland region. [source] Assembling the stratigraphic record: depositional patterns and time-scales in an experimental alluvial basinBASIN RESEARCH, Issue 3 2002B. A. Sheets ABSTRACT Our understanding of sedimentation in alluvial basins is best for very short and very long time-scales (those of bedforms to bars and basinwide deposition, respectively). Between these end members, the intermediate time-scales of stratigraphic assembly are especially hard to constrain with field data. We address these ,mesoscale' fluvial dynamics with data from an experimental alluvial system in a basin with a subsiding floor. Observations of experimental deposition over a range of time-scales illustrate two important properties of alluvial systems. First, ephemeral flows are disproportionately important in basin filling. Lack of correlation between flow occupation and sedimentation indicates that channelized flows serve mainly as conduits for sediment, while most deposition occurs via short-lived unchannelized flow events. Second, there is a characteristic time required for individual depositional events to average to basin-scale stratal patterns. This time can be scaled in terms of the time required for a single channel-depth of aggradation, and in this form is constant through a four-fold variation of experimental subsidence rate. [source] | ||||||||||