The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Indian Ocean Dipole: Processes and impacts

Equatorial Indian Ocean is warmer in the east, has a deeper thermocline and mixed layer, and supports a more convective atmosphere than in the west. During certain years, the eastern Indian Ocean becomes unusually cold, anomalous winds blow from east to west along the equator and southeastward off the coast of Sumatra, thermocline and mixed layer lift up and the atmospheric convection gets suppressed. At the same time, western Indian Ocean becomes warmer and enhances atmospheric convection. This coupled ocean-atmospheric phenomenon in which convection, winds, sea surface temperature (SST) and thermocline take part actively is known as the Indian Ocean Dipole (IOD). Propagation of baroclinic Kelvin and Rossby waves excited by anomalous winds, play an important role in the development of SST anomalies associated with the IOD. Since mean thermocline in the Indian Ocean is deep compared to the Pacific, it was believed for a long time that the Indian Ocean is passive and merely responds to the atmospheric forcing. Discovery of the IOD and studies that followed demonstrate that the Indian Ocean can sustain its own intrinsic coupled ocean-atmosphere processes. About 50% percent of the IOD events in the past 100 years have co-occurred with El Nino Southern Oscillation (ENSO) and the other half independently. Coupled models have been able to reproduce IOD events and process experiments by such models – switching ENSO on and off – support the hypothesis based on observations that IOD events develop either in the presence or absence of ENSO. There is a general consensus among different coupled models as well as analysis of data that IOD events co-occurring during the ENSO are forced by a zonal shift in the descending branch of Walker cell over to the eastern Indian Ocean. Processes that initiate the IOD in the absence of ENSO are not clear, although several studies suggest that anomalies of Hadley circulation are the most probable forcing function. Impact of the IOD is felt in the vicinity of Indian Ocean as well as in remote regions. During IOD events, biological productivity of the eastern Indian Ocean increases and this in turn leads to death of corals over a large area.Moreover, the IOD affects rainfall over the maritime continent, Indian subcontinent, Australia and eastern Africa. The maritime continent and Australia suffer from deficit rainfall whereas India and east Africa receive excess. Despite the successful hindcast of the 2006 IOD by a coupled model, forecasting IOD events and their implications to rainfall variability remains a major challenge as understanding reasons behind an increase in frequency of IOD events in recent decades.

Dynamic analysis of three point bend specimens under impact

A simple one dimensional inertial model is presented for transient response analysis of notched beams under impact, and extracting dynamic initiation toughness values. The model includes the effects of striker mass interactions, and contact deformations of the beam. Displacement time history of the striker mass is applied to the model as forcing function. The model is validated by comparison with the experimental investigation on ductile aluminium 6061 alloy and brittle polymer, PMMA.

Spectral density of first order Piecewise linear systems excited by white noise

The Fokker-Planck (FP) equation is used to develop a general method for finding the spectral density for a class of randomly excited first order systems. This class consists of systems satisfying stochastic differential equations of form ẋ + f(x) = m/Ʃ/j = 1 h_j(x)n_j(t) where f and the h_j are piecewise linear functions (not necessarily continuous), and the n_j are stationary Gaussian white noise. For such systems, it is shown how the Laplace-transformed FP equation can be solved for the transformed transition probability density. By manipulation of the FP equation and its adjoint, a formula is derived for the transformed autocorrelation function in terms of the transformed transition density. From this, the spectral density is readily obtained. The method generalizes that of Caughey and Dienes, J. Appl. Phys., 32.11.

This method is applied to 4 subclasses: (1) m = 1, h₁ = const. (forcing function excitation); (2) m = 1, h₁ = f (parametric excitation); (3) m = 2, h₁ = const., h₂ = f, n₁ and n₂ correlated; (4) the same, uncorrelated. Many special cases, especially in subclass (1), are worked through to obtain explicit formulas for the spectral density, most of which have not been obtained before. Some results are graphed.

Dealing with parametrically excited first order systems leads to two complications. There is some controversy concerning the form of the FP equation involved (see Gray and Caughey, J. Math. Phys., 44.3); and the conditions which apply at irregular points, where the second order coefficient of the FP equation vanishes, are not obvious but require use of the mathematical theory of diffusion processes developed by Feller and others. These points are discussed in the first chapter, relevant results from various sources being summarized and applied. Also discussed is the steady-state density (the limit of the transition density as t → ∞).

A Theoretical and Experimental Study of Resonance in a High Performance Engine Intake System: Part 1

The unsteady gas dynamic phenomena in engine intake systems of the type found in racecars have been examined. In particular, the resonant tuning effects, including cylinder-to-cylinder power variations, which can occur as a result of the interaction between an engine and its airbox have been considered. Frequency analysis of the output from a Virtual 4-Stroke 1D engine simulation was used to characterise the forcing function applied by an engine to an airbox. A separate computational frequency sweeping technique, which employed the CFD package FLUENT, was used to determine the natural frequencies of virtual airboxes in isolation from an engine. Using this technique, an airbox with a natural frequency at 75 Hz was designed for a Yamaha R6 4-cylinder motorcycle engine. The existence of an airbox natural frequency at 75 Hz was subsequently confirmed by an experimental frequency sweeping technique carried out on the engine test bed. A coupled 1D/3D analysis which employed the engine simulation package Virtual 4-Stroke and the CFD package FLUENT, was used to model the combined engine and airbox system. The coupled 1D/3D analysis predicted a 75 Hz resonance of the airbox at an engine speed of 9000 rpm. This frequency was the induction frequency for a single cylinder. An airbox was fabricated and tested on the engine. Static pressure was recorded at a grid of points in the airbox as the engine was swept through a speed range of 3000 to 10000 rpm. The measured engine speed corresponding to resonance in the airbox agreed well with the predicted values. There was also good correlation between the amplitude and phase of the pressure traces recorded within the airbox and the 1D/3D predictions.

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

Avaliação limnológica em um sistema de piscicultura na região de Paranaíta (MT, Brasil)

Pós-graduação em Aquicultura - FCAV

Maremoti in bacini limitati

The work of my thesis is focused on the impact of tsunami waves in limited basins. By limited basins I mean here those basins capable of modifying significantly the tsunami signal with respect to the surrounding open sea. Based on this definition, we consider limited basins not only harbours but also straits, channels, seamounts and oceanic shelves. I have considered two different examples, one dealing with the Seychelles Island platform in the Indian Ocean, the second focussing on the Messina Strait and the harbour of the Messina city itself (Italy). The Seychelles platform is differentiated at bathymetric level from the surrounding ocean, with rapid changes from 2 km to 70 meters over short horizontal distances. The study of the platform response to the tsunami propagation is based on the simulation of the mega-event occurred on 26 December 2004. Based on a hypothesis for the earthquake causative fault, the ensuing tsunami has been numerically simulated. I analysed synthetic tide gauge records at several virtual tide gauges aligned along the direction going from the source to the platform. A substantial uniformity of tsunami signals in all calculated open ocean tide-gauge records is observed, while the signals calculated in two points of the Seychelles platform show different features both in terms of amplitude and period of the perturbation. To better understand the content in frequency of different calculated marigrams, a spectral analysis was carried out. In particular the ratio between the calculated tide-gauge records spectrum on the platform and the average tide-gauge records in the open ocean was considered. The main result is that, while in the average spectrum in the open ocean the fundamental peak is related to the source, the platform introduces further peaks linked both to the bathymetric configuration and to coastal geometry. The Messina Strait represents an interesting case because it consists in a sort of a channel open both in the north and in the south and furthermore contains the limited basin of the Messina harbour. In this case the study has been carried out in a different way with respect to the Seychelles case. The basin was forced along a boundary of the computational domain with sinusoidal functions having different periods within the typical tsunami frequencies. The tsunami has been simulated numerically and in particular the tide-gauge records were calculated for every forcing function in different points both externally and internally of the channel and of the Messina harbour. Apart from the tide-gauge records in the source region that almost immediately reach stationarity, all the computed signals in the channel and in the Messina harbour present a transient variable amplitude followed by a stationary part. Based exclusively on this last part, I calculated the amplification curves for each site. I found that the maximum amplification is obtained for forcing periods of approximately 10 minutes.

Development of an In Situ Measurement Device for Obtaining Material Thermal Properties

This thesis presents a methodology for measuring thermal properties in situ, with a special focus on obtaining properties of layered stack-ups commonly used in armored vehicle components. The technique involves attaching a thermal source to the surface of a component, measuring the heat flux transferred between the source and the component, and measuring the surface temperature response. The material properties of the component can subsequently be determined from measurement of the transient heat flux and temperature response at the surface alone. Experiments involving multilayered specimens show that the surface temperature response to a sinusoidal heat flux forcing function is also sinusoidal. A frequency domain analysis shows that sinusoidal thermal excitation produces a gain and phase shift behavior typical of linear systems. Additionally, this analysis shows that the material properties of sub-surface layers affect the frequency response function at the surface of a particular stack-up. The methodology involves coupling a thermal simulation tool with an optimization algorithm to determine the material properties from temperature and heat flux measurement data. Use of a sinusoidal forcing function not only provides a mechanism to perform the frequency domain analysis described above, but sinusoids also have the practical benefit of reducing the need for instrumentation of the backside of the component. Heat losses can be minimized by alternately injecting and extracting heat on the front surface, as long as sufficiently high frequencies are used.

Changes in bottom water corrosiveness and carbonate ion concentrations in the sub-Antarctic Atlantic during the last glacial period

The glacial climate system transitioned rapidly between cold (stadial) and warm (interstadial) conditions in the Northern Hemisphere. This variability, referred to as Dansgaard-Oeschger variability, is widely believed to arise from perturbations of the Atlantic Meridional Overturning Circulation. Evidence for such changes during the longer Heinrich stadials has been identified, but direct evidence for overturning circulation changes during Dansgaard-Oeschger events has proven elusive. Here we reconstruct bottom water [CO3]2- variability from B/Ca ratios of benthic foraminifera and indicators of sedimentary dissolution, and use these reconstructions to infer the flow of northern-sourced deep water to the deep central sub-Antarctic Atlantic Ocean. We find that nearly every Dansgaard-Oeschger interstadial is accompanied by a rapid incursion of North Atlantic Deep Water into the deep South Atlantic. Based on these results and transient climate model simulations, we conclude that North Atlantic stadial-interstadial climate variability was associated with significant Atlantic overturning circulation changes that were rapidly transmitted across the Atlantic. However, by demonstrating the persistent role of Atlantic overturning circulation changes in past abrupt climate variability, our reconstructions of carbonate chemistry further indicate that the carbon cycle response to abrupt climate change was not a simple function of North Atlantic overturning.

Physical oceanography during five ECOMARGE cruises

The first experiment of the ECOMARGE programme (ECOsystèmes de MARGE continentale) was initiated in 1983-1984, in the Gulf of Lions (northwestern Mediterranean Sea). The objectives of the ECOMARGE-I experiment were: to quantify the transfer of particulate matter, in general, and of organic carbon, in particular, from its introduction to and formation in the waters of the continental shelf-to its consumption or sedimentation on the shelf or its transfer to the slope and deep sea; and to understand the processes involved in that transfer, consumption and sedimentation together with their variability in space and time. The results of that experiment, from 1983 to 1988, are presented in this Special Issue. The highlights of the results are summarised in this paper. These results indicate that, of the particles formed in the waters of the continental shelf and those introduced by rivers, some are deposited as sediments on the shelf. A portion is transported offshore, however, to the slope and deep sea. The Rho^ne River, in the northeastern part of the study area, is the major source of continental material; this is transported to sea in a benthic nepheloid layer and, mostly, alongshore to the southwest. Here, it largely leaves the shelf through the canyons, especially the Lacaze-Duthiers Canyon. In the offshore waters, particle concentrations and distributions show surficial, intermediate and benthic nepheloid layers. These turbid structures increase towards the southwest, corresponding to the seaward shift of the front between the coastal waters and the Liguro-Provençal cyclonic gyre, a major forcing function in the Gulf of Lions. Considering the source and fate of particles (largely biogenic from the euphotic zone and abiogenic from deeper waters) a layered system is described, which is emphasized by the concentrations of natural and artificial elements and compounds. Of the flux of particles to the Lacaze-Duthiers Canyon, on a decadal scale, about 30% (as a minimum) is estimated to be stored as sediment; the remainder is transported down-canyon, towards the deep sea. The temporal variability of processes affecting this net seaward transport, of both biogenic and abiogenic material, is from hours, days to seasonal, and probably interannual, time scales. The response of the system to these variations is rapid, with pulses of increased discharge of particles from the adjacent shelf being detected in sediment traps in the Lacaze-Duthiers Canyon in less than 16 days (the temporal resolution of the traps). Based upon the study of tracers of particulate matter and environmental factors (i.e. river discharge and climatic conditions), it appears that the contribution from the Rho^ne River and its adjacent area is maximal during the winter; at this time, the flow of the Liguro-Provençal Current also increases. In contrast, the maximum relative contribution of the adjacent southwesterly area to the flux in the Lacaze-Duthiers Canyon occurs in summer, during storm events.

Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^