Contribution of tectonic processes to the exhumation of the Cycladic blueschist unit, Greece and Turkey

In dieser Studie werden strukturgeologische, metamorphe und geochronologische Daten benutzt, um eine Quantifizierung tektonischer Prozesse vorzunehmen, die für die Exhumierung der Kykladischen Blauschiefereinheit in der Ägäis und der Westtürkei verantwortlich waren. Bei den beiden tektonischen Prozessen handelt es sich um: (1) Abschiebungstektonik und (2) vertikale duktile Ausdünnung. Eine finite Verformungsanalyse an Proben der Kykladischen Blauschiefereinheit ermöglicht eine Abschätzung des Beitrags von vertikaler duktiler Ausdünnung an der gesamten Exhumierung. Kalkulationen mit einem eindimensionalen, numerischen Model zeigt, daß vertikale duktile Ausdünnung nur ca. 10% an der gesamten Exhumierung ausmacht. Kinematische, metamorphe und geochronologische Daten erklären die tektonische Natur und die Evolution eines extensionalen Störungssystems auf der Insel Ikaria in der östlichen Ägäis. Thermobarometrische Daten lassen erkennen, daß das Liegende des Störungssystems aus ca. 15 km Tiefe exhumiert wurde. Sowohl Apatit- und Zirkonspaltspurenalter als auch Apatit (U-Th)/He-Alter zeigen, daß sich das extensionale Störungssystem zwischen 11-3 Ma mit einer Geschwindigkeit von ca. 7-8 km/Ma bewegte. Spät-Miozäne Abschiebungen trugen zur Exhumierung der letzten ~5-15 km der Hochdruckgesteine bei. Ein Großteil der Exhumierung der Kykladischen Blauschiefereinheit muß vor dem Miozän stattgefunden haben. Dies wird durch einen Extrusionskeil erklärt, der ca. 30-35 km der Kykladischen Blauschiefereinheit in der Westtürkei exhumierte. 40Ar/39Ar und 87Rb/86Sr Datierungen an Myloniten des oberen Abschiebungskontakts zwischen der Selçuk Decke und der darunterliegenden Ampelos/Dilek Decke der Kykladischen Blauschiefereinheit als auch des unteren Überschiebungskontakts zwischen der Ampelos/Dilek Decke und den darunterliegenden Menderes Decken zeigt, daß sich beide mylonitische Zonen um ca. ~35 Ma formten, was die Existenz eines Spät-Eozänen/Früh-Oligozänen Extrusionskeils beweist.

Influences of deep convective cloud systems on tropospheric trace gases and photochemistry over the tropical West Pacific

A numerical model for studying the influences of deep convective cloud systems on photochemistry was developed based on a non-hydrostatic meteorological model and chemistry from a global chemistry transport model. The transport of trace gases, the scavenging of soluble trace gases, and the influences of lightning produced nitrogen oxides (NOx=NO+NO2) on the local ozone-related photochemistry were investigated in a multi-day case study for an oceanic region located in the tropical western Pacific. Model runs considering influences of large scale flows, previously neglected in multi-day cloud resolving and single column model studies of tracer transport, yielded that the influence of the mesoscale subsidence (between clouds) on trace gas transport was considerably overestimated in these studies. The simulated vertical transport and scavenging of highly soluble tracers were found to depend on the initial profiles, reconciling contrasting results from two previous studies. Influences of the modeled uptake of trace gases by hydrometeors in the liquid and the ice phase were studied in some detail for a small number of atmospheric trace gases and novel aspects concerning the role of the retention coefficient (i.e. the fraction of a dissolved trace gas that is retained in the ice phase upon freezing) on the vertical transport of highly soluble gases were illuminated. Including lightning NOx production inside a 500 km 2-D model domain was found to be important for the NOx budget and caused small to moderate changes in the domain averaged ozone concentrations. A number of sensitivity studies yielded that the fraction of lightning associated NOx which was lost through photochemical reactions in the vicinity of the lightning source was considerable, but strongly depended on assumptions about the magnitude and the altitude of the lightning NOx source. In contrast to a suggestion from an earlier study, it was argued that the near zero upper tropospheric ozone mixing ratios which were observed close to the study region were most probably not caused by the formation of NO associated with lightning. Instead, it was argued in agreement with suggestions from other studies that the deep convective transport of ozone-poor air masses from the relatively unpolluted marine boundary layer, which have most likely been advected horizontally over relatively large distances (both before and after encountering deep convection) probably played a role. In particular, it was suggested that the ozone profiles observed during CEPEX (Central Equatorial Pacific Experiment) were strongly influenced by the deep convection and the larger scale flow which are associated with the intra-seasonal oscillation.

The development of stylolites, from small-scale heterogeneities to multi-scale roughness

Stylolites are rough paired surfaces, indicative of localized stress-induced dissolution under a non-hydrostatic state of stress, separated by a clay parting which is believed to be the residuum of the dissolved rock. These structures are the most frequent deformation pattern in monomineralic rocks and thus provide important information about low temperature deformation and mass transfer. The intriguing roughness of stylolites can be used to assess amount of volume loss and paleo-stress directions, and to infer the destabilizing processes during pressure solution. But there is little agreement on how stylolites form and why these localized pressure solution patterns develop their characteristic roughness.rnNatural bedding parallel and vertical stylolites were studied in this work to obtain a quantitative description of the stylolite roughness and understand the governing processes during their formation. Adapting scaling approaches based on fractal principles it is demonstrated that stylolites show two self affine scaling regimes with roughness exponents of 1.1 and 0.5 for small and large length scales separated by a crossover length at the millimeter scale. Analysis of stylolites from various depths proved that this crossover length is a function of the stress field during formation, as analytically predicted. For bedding parallel stylolites the crossover length is a function of the normal stress on the interface, but vertical stylolites show a clear in-plane anisotropy of the crossover length owing to the fact that the in-plane stresses (σ2 and σ3) are dissimilar. Therefore stylolite roughness contains a signature of the stress field during formation.rnTo address the origin of stylolite roughness a combined microstructural (SEM/EBSD) and numerical approach is employed. Microstructural investigations of natural stylolites in limestones reveal that heterogeneities initially present in the host rock (clay particles, quartz grains) are responsible for the formation of the distinctive stylolite roughness. A two-dimensional numerical model, i.e. a discrete linear elastic lattice spring model, is used to investigate the roughness evolving from an initially flat fluid filled interface induced by heterogeneities in the matrix. This model generates rough interfaces with the same scaling properties as natural stylolites. Furthermore two coinciding crossover phenomena in space and in time exist that separate length and timescales for which the roughening is either balanced by surface or elastic energies. The roughness and growth exponents are independent of the size, amount and the dissolution rate of the heterogeneities. This allows to conclude that the location of asperities is determined by a polimict multi-scale quenched noise, while the roughening process is governed by inherent processes i.e. the transition from a surface to an elastic energy dominated regime.rn

Untersuchungen zur Genauigkeit adaptiver unstetiger Galerkin-Simulationen mit Hilfe von Luftblasen-Testfällen

Allgemein erlaubt adaptive Gitterverfeinerung eine Steigerung der Effizienz numerischer Simulationen ohne dabei die Genauigkeit des Ergebnisses signifikant zu verschlechtern. Es ist jedoch noch nicht erforscht, in welchen Bereichen des Rechengebietes die räumliche Auflösung tatsächlich vergröbert werden kann, ohne die Genauigkeit des Ergebnisses signifikant zu beeinflussen. Diese Frage wird hier für ein konkretes Beispiel von trockener atmosphärischer Konvektion untersucht, nämlich der Simulation von warmen Luftblasen. Zu diesem Zweck wird ein neuartiges numerisches Modell entwickelt, das auf diese spezielle Anwendung ausgerichtet ist. Die kompressiblen Euler-Gleichungen werden mit einer unstetigen Galerkin Methode gelöst. Die Zeitintegration geschieht mit einer semi-implizite Methode und die dynamische Adaptivität verwendet raumfüllende Kurven mit Hilfe der Funktionsbibliothek AMATOS. Das numerische Modell wird validiert mit Hilfe einer Konvergenzstudie und fünf Standard-Testfällen. Eine Methode zum Vergleich der Genauigkeit von Simulationen mit verschiedenen Verfeinerungsgebieten wird eingeführt, die ohne das Vorhandensein einer exakten Lösung auskommt. Im Wesentlichen geschieht dies durch den Vergleich von Eigenschaften der Lösung, die stark von der verwendeten räumlichen Auflösung abhängen. Im Fall einer aufsteigenden Warmluftblase ist der zusätzliche numerische Fehler durch die Verwendung der Adaptivität kleiner als 1% des gesamten numerischen Fehlers, wenn die adaptive Simulation mehr als 50% der Elemente einer uniformen hoch-aufgelösten Simulation verwendet. Entsprechend ist die adaptive Simulation fast doppelt so schnell wie die uniforme Simulation.

Potential vorticity and moisture in extratropical cyclones : climatology and sensitivity experiments

The development of extratropical cyclones can be seen as an interplay of three positive potential vorticity (PV) anomalies: an upper-level stratospheric intrusion, low-tropospheric diabatically produced PV, and a warm anomaly at the surface acting as a surrogate PV anomaly. In the mature stage they become vertically aligned and form a “PV tower” associated with strong cyclonic circulation. This paradigm of extratropical cyclone development provides the basis of this thesis, which will use a climatological dataset and numerical model experiments to investigate the amplitude of the three anomalies and the processes leading in particular to the formation of the diabatically produced low-tropospheric PV anomaly.rnrnThe first part of this study, based on the interim ECMWF Re-Analysis (ERA-Interim) dataset, quantifies the amplitude of the three PV anomalies in mature extratropical cyclones in different regions in the Northern Hemisphere on a climatological basis. A tracking algorithm is applied to sea level pressure (SLP) fields to identify cyclone tracks. Surface potential temperature anomalies ∆θ and vertical profiles of PV anomalies ∆PV are calculated at the time of the cyclones’ minimum SLP and during the intensification phase 24 hours before in a vertical cylinder with a radius of 200 km around the surface cyclone center. To compare the characteristics of the cyclones, they are grouped according to their location (8 regions) and intensity, where the central SLP is used as a measure of intensity. Composites of ∆PV profiles and ∆θ are calculated for each region and intensity class at the time of minimum SLP and during the cyclone intensification phase.rnrnDuring the cyclones’ development stage the amplitudes of all three anomalies increase on average. In the mature stage all three anomalies are typically larger for intense than for weak winter cyclones [e.g., 0.6 versus 0.2 potential vorticity units (PVU) at lower levels, and 1.5 versus 0.5 PVU at upper levels].rnThe regional variability of the cyclones’ vertical structure and the profile evolution is prominent (cyclones in some regions are more sensitive to the amplitude of a particular anomaly than in other regions). Values of ∆θ and low-level ∆PV are on average larger in the western parts of the oceans than in the eastern parts. In addition, a large seasonal variability can be identified, with fewer and weaker cyclones especially in the summer, associated with higher low-tropospheric PV values, but also with a higher tropopause and much weaker surface potential temperature anomalies (compared to winter cyclones).rnrnIn the second part, we were interested in the diabatic low-level part of PV towers. Evaporative sources were identified of moisture that was involved in PV production through condensation. Lagrangian backward trajectories were calculated from the region with high PV values at low-levels in the cyclones. PV production regions were identified along these trajectories and from these regions a new set of backward trajectories was calculated and moisture uptakes were traced along them. The main contribution from surface evaporation to the specific humidity of the trajectories is collected 12-72 hours prior to therntime of PV production. The uptake region for weaker cyclones with less PV in the centre is typically more localized with reduced uptake values compared to intense cyclones. However, in a qualitative sense uptakes and other variables along single trajectories do not vary much between cyclones of different intensity in different regions.rnrnA sensitivity study with the COSMO model comprises the last part of this work. The study aims at investigating the influence of synthetic moisture modification in the cyclone environment in different stages of its development. Moisture was eliminated in three regions, which were identified as important moisture source regions for PV production. Moisture suppression affected the cyclone the most in its early phase. It led to cyclolysis shortly after its genesis. Nevertheles, a new cyclone formed on the other side of a dry box and developed relatively quickly. Also in other experiments, moisture elimination led to strong intensity reduction of the surface cyclone, limited upper-level development, and delayed or missing interaction between the two.rnrnIn summary, this thesis provides novel insight into the structure of different intensity categories of extratropical cyclones from a PV perspective, which corroborates the findings from a series of previous case studies. It reveals that all three PV anomalies are typically enhanced for more intense cyclones, with important regional differences concerning the relative amplitude of the three anomalies. The moisture source analysis is the first of this kind to study the evaporation-condensation cycle related to the intensification of extratropical cyclones. Interestingly, most of the evaporation occurs during the 3 days prior to the time of maximum cyclone intensity and typically extends over fairly large areas along the track of the cyclone. The numerical model case study complements this analysis by analyzing the impact of regionally confined moisture sources for the evolution of the cyclone.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.