Direct velocity measurement of a turbulent shear flow in a planar Couette cell

In a plane Couette cell a thin fluid layer consisting of water is sheared between a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cells flow channel is large compared to the film separation. To extract the flow velocity in the experiments a correlation image velocimetry (CIV) method is used on pictures recorded with a high speed camera. The flow is recorded at a resolution that allows to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent pattern that arise on this scale above a critical Reynolds number of Re=360 display characteristic patterns that are proven with the calculated velocity autocorrelation functions. The patterns are metastable and reappear at different positions and times throughout the experiments. Typically these patterns are turbulent rolls which are elongated in the stream direction which is the direction the band is moving. Although the flow states are metastable they possess similarities to the steady Taylor vortices known to appear in circular Taylor Couette cells

Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.Comment: Physical Review E (2011); 62.20.mt, 46.50.+a, 68.35.C

Eksisterer det en weekendvolatilitet i det nordiske finansielle kraftmarkedet?

Denne masterutredningen undersøker hvorvidt det eksisterer en weekendvolatilitet i det nordiske finansielle kraftmarkedet. Analysen tar utgangspunkt i daglige sluttkurser for forwardkontrakter med leveringsperiode et kvartal og et år. De to kontraktstypene analyseres hver for seg. Vi gjennomfører også en kort analyse av volatiliteten på underliggende spotpris. Resultatene våre viser at denne er svært volatil og en kjøper eller en selger av nordisk kraft vil derfor utsettes for høy prisrisiko ved å ha en usikret posisjon. Volatiliteten i de finansielle kontraktene er imidlertid betydelig lavere enn volatiliteten til spotprisen. Gitt en forutsetning om at markedet for omsetting av forwardkontraktene er effisient kan variansen for lørdag og søndag estimeres med utgangspunkt i totalvariansen for sluttkursen fredag og sluttkursen mandag. Resultatene viser at det, gitt våre forutsetninger, eksisterer en volatilitet på lørdag og søndag til tross for at de finansielle kontraktene ikke omsettes i helgen. Volatiliteten for lørdag og søndag reflekteres derfor i prisendringene på mandag. Resultatene fra analysen av weekendvolatiliteten brukes videre til å illustrere tre typer tilnærminger til Value at Risk, henholdsvis historisk metode, parametrisk metode og Monte Carlo-simulering. Med dette ønsker vi å vise i hvilken grad Value at Risk kan betraktes som et godt estimat på potensielle tap i dette markedet. Vi bruker også Conditional Value at Risk (Expected Shortfall) som kan gi et mer nyansert bilde av prisrisikoen. Til slutt illustreres konsekvensene for prising av opsjoner med kort løpetid ved bruk av ulike volatilitetsestimater. I denne oppgaven defineres kort løpetid som opsjoner med løpetid på maks seks ukedager. Vi bruker Black -76 opsjonsprisingsmodell for prising av opsjoner på kvartalskontrakter og årskontrakter og finner store avvik i prosentvise prisforskjeller for out-of-themoney opsjoner. In this thesis we analyze the weekend volatility in the Nordic financial power market. The analysis uses daily closing prices for forward contracts with delivery period of one quarter and one year respectively. The two different categories of contracts are analyzed separately. To be able to compare the volatility of the financial contracts with the underlying spot price we also exhibit an analysis of the underlying spot price. Our results show that this is highly volatile, implying that an unhedged buyer or seller of Nordic power is exposed to major price risk. The volatility of the financial contracts, however, is significantly lower than the volatility of the spot price. Given the assumption of efficient markets in the buying and selling of forward contracts, the variance for Saturday and Sunday can be estimated by using the variance from Friday close to Monday close. The results indicate, given our assumptions, that there is some volatility on Saturday and Sunday, despite the fact that the financial markets are closed during the weekends. The volatility for Saturday and Sunday is therefore reflected in the price changes on Monday. The results from the analysis of the weekend volatility are further used to estimate different Value at Risk measures based on three different methods. These are the historical method, the parametric method and Monte Carlo simulation. The results are used to illustrate to what extent Value at Risk adequately estimates the potential loss in this market. We also use Conditional Value at Risk (Expected Shortfall) which may give a better estimate of the actual price risk. Finally, we illustrate the consequences for the pricing of shorter term options when different measures of volatility are used. In this thesis, we define shorter term options as options with maturity of six days or less.We use the Black-76 model to price options on quarterly and yearly contracts and find that the relative price differences are significant for out-of-the-money options

Average crack-front velocity during subcritical fracture propagation in a heterogeneous medium

We study the average velocity of crack fronts during stable interfacial fracture experiments in a heterogeneous quasibrittle material under constant loading rates and during long relaxation tests. The transparency of the material (polymethylmethacrylate) allows continuous tracking of the front position and relation of its evolution to the energy release rate. Despite significant velocity fluctuations at local scales, we show that a model of independent thermally activated sites successfully reproduces the large-scale behavior of the crack front for several loading conditions

The non-Gaussian nature of fracture and the survival of fat-tail exponents

4 pagesInternational audienceWe study the fluctuations of the global velocity Vl(t), computed at various length scales l, during the intermittent Mode-I propagation of a crack front. The statistics converge to a non-Gaussian distribution, with an asymmetric shape and a fat tail. This breakdown of the Central Limit Theorem (CLT), is due to the diverging variance of the underlying local crack front velocity distribution, displaying a power law tail. Indeed, by the application of a generalized CLT, the full shape of our experimental velocity distribution at large scale is shown to follow the stable Levy distribution, which preserves the power law tail exponent under upscaling. This study aims to demonstrate in general for Crackling Noise systems, how one can infer the complete scale dependence of the activity- and extreme event distributions, by measuring only at a global scale

Influence of water pressure dynamics and fluid flow on the streaming-potential response for unsaturated conditions

International audienceA B S T R A C T Streaming-potentials are produced by electrokinetic effects in relation to fluid flow and are used for geophysical prospecting. The aim of this study is to model streaming potential measurements for unsaturated conditions using an empirical approach. A conceptual model is applied to streaming potential measurements obtained from two drainage experiments in sand. The streaming potential data presented here show a non-monotonous behaviour with increasing water saturation, following a pattern that cannot be predicted by existing models. A model involving quasi-static and dynamic components is proposed to reproduce the streaming potential measurements. The dynamic component is based on the first time derivative of the driving pore pressure. The influence of this component is investigated with respect to fluid velocity, which is very different between the two experiments. The results demonstrate that the dynamic component is predominant at the onset of drainage in experiments with the slowest water flow. On the other hand, its influence appears to vanish with increasing drainage velocity. Our results suggest that fluid flow and water distribution at the pore scale have an important influence on the streaming potential response for unsat-urated conditions. We propose to explain this specific streaming potential response in terms of the behaviour of both rock/water interface and water/air interfaces created during desaturation processes. The water/air interfaces are negatively charged, as also observed in the case of water/rock interfaces. Both the surface area and the flow velocity across these interfaces are thought to contribute to the non-monotonous behaviour of the streaming potential coefficient as well as the variations in its amplitude. The non-monotonous behaviour of air/water interfaces created during the flow was highlighted as it was measured and modelled by studies published in the literature. The streaming potential coefficient can increase to about 10 to 40 when water saturation decreases. Such an increase is possible if the amount of water/air interfaces is increased in sufficient amount, which can be the case

X-ray Microtomography of Intermittency in Multiphase Flow at Steady State Using a Differential Imaging Method

We imaged the steady state flow of brine and decane in Bentheimer sandstone. We devised an experimental method based on differential imaging to examine how flow rate impacts impact the pore-scale distribution of fluids during coinjection. This allows us to elucidate flow regimes (connected, or breakup of the nonwetting phase path ways) for a range of fractional flows at two capillary numbers, Ca, namely 3.0 × 10 −7 and 7.5 × 10 −6 . At the lower Ca, for a fixed fractional flow, the two phases appear to flow in connected unchanging subnetworks of the pore space, consistent with conventional theory. At the higher Ca, we observed that a significant fraction of the pore space contained sometimes oil and sometimes brine during the 1 h scan: this intermittent occupancy, which was interpreted as regions of the pore space that contained both fluid phases for some time, is necessary to explain the flow and dynamic connectivity of the oil phase; pathways of always oil-filled portions of the void space did not span the core. This phase was segmented from the differential image between the 30 wt % KI brine image and the scans taken at each fractional flow. Using the grey scale histogram distribution of the raw images, the oil proportion in the intermittent phase was calculated. The pressure drops at each fractional flow at low and high flow rates were measured by high-precision differential pressure sensors. The relative permeabilities and fractional flow obtained by our experiment at the mm-scale compare well with data from the literature on cm-scale samples

Disordered Elastic Systems and One-Dimensional Interfaces

We briefly introduce the generic framework of Disordered Elastic Systems (DES), giving a short `recipe' of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. We then focus on a particular low-dimensional DES, namely the one-dimensional interface in short-ranged elasticity and short-ranged quenched disorder. Illustrating different elements given in the introductory sections, we discuss specifically the consequences of the interplay between a finite temperature T>0 and a finite interface width \xi>0 on the static geometrical fluctuations at different lengthscales, and the implications on the quasistatic dynamics.Comment: Proceedings of the International Workshop on Electronic Crystals (ECRYS), Cargese (2011

Steady-state two-phase flow in porous media: statistics and transport properties.

We study experimentally the case of steady-state simultaneous two-phase flow in a quasi-two-dimensional porous media. The dynamics is dominated by the interplay between a viscous pressure field from the wetting fluid and bubble transport of a less viscous, nonwetting phase. In contrast with more studied displacement front systems, steady-state flow is in equilibrium, statistically speaking. The corresponding theoretical simplicity allows us to explain a data collapse in the cluster size distribution as well as the relation |nablaP| proportional, sqrt[Ca] between the pressure gradient in the system and the capillary number