Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Early Eocene benthic foraminifera of DSDP Hole 48-401

Within the last decade, several early Eocene hyperthermals have been detected globally. These transient warming events have mainly been characterized geochemically - using stable isotopes, carbonate content measurements or XRF core scanning - yet detailed micropaleontological records are sparse, limiting our understanding of the driving forces behind hyperthermals and of the contemporaneous paleoceanography. Here, detailed geochemical and quantitative benthic foraminiferal records are presented from lower Eocene pelagic sediments of Deep Sea Drilling Project Site 401 (Bay of Biscay, northeast Atlantic). In calcareous nannofossil zone NP11, several clay-enriched levels correspond to negative d13C and d18O bulk-rock excursions with amplitudes of up to ~0.75 per mil, suggesting that significant injections of 12C-enriched greenhouse gasses and small temperature rises took place. Coeval with several of these hyperthermal events, the benthic foraminiferal record reveals increased relative abundances of oligotrophic taxa (e.g. Nuttallides umbonifera) and a reduction in the abundance of buliminid species followed by an increase of opportunistic taxa (e.g. Globocassidulina subglobosa and Gyroidinoides spp.). These short-lived faunal perturbations are thought to be caused by reduced seasonality of productivity resulting in a decreased Corg flux to the seafloor. Moreover, the sedimentological record suggests that an enhanced influx of terrigenous material occurred during these events. Additionally, the most intense d13C decline (here called level d) gives rise to a small, yet pronounced long-term shift in the benthic foraminiferal composition at this site, possibly due to the reappraisal of upwelling and the intensification of bottom water currents. These observations imply that environmental changes during (smaller) hyperthermal events are also reflected in the composition of deep-sea benthic communities on both short (<100 kyr) and longer time scales. We conclude that the faunal patterns of the hyperthermals observed at Site 401 strongly resemble those observed in other deep-sea early Paleogene hyperthermal deposits, suggesting that similar processes have driven them.

Magnetic measurements on ODP holes 178-1095A, 178-1095B and 178-1101A

We have determined the azimuth of bottom-current flow in drift deposit sediments recovered at ODP Sites 1095 and 1101, Antarctic Peninsula, using paleomagnetic reorientation of anisotropy of magnetic susceptibility (AMS) ellipsoids. A total of 38 cores from the two ODP sites have been measured, providing spatial and directional information on the physical record of the ACC (Antarctic Circumpolar Current) in the Plio-Pleistocene. Declination and inclination of the paleomagnetic vector of each core segment were used to reorient the AMS principal axes to the geographic coordinates. The cores were reoriented using the measured direction of the characteristic remanent magnetization (ChRM) with respect to a common reference line for the core, from which we are able to determine the orientation of the paleocurrent flow for Sites 1095 (Drift 7) and 1101 (Drift 4) relative to the geographic coordinates. Both sites have paleocurrent directions trending ~NW-SE, which in the former locality are parallel to a sediment wave field. Our study shows that a combination of magnetic fabric analysis and paleomagnetism allows deep-sea sedimentary fabric to be used as a long-term proxy of bottom-current flow history.

Paleomagnetic and rock magnetic properties of IODP Expedition 318 cores

The Integrated Ocean Drilling Program Expedition 318 to the Wilkes Land margin of Antarctica recovered a sedimentary succession ranging in age from lower Eocene to the Holocene. Excellent stratigraphic control is key to understanding the timing of paleoceanographic events through critical climate intervals. Drill sites recovered the lower and middle Eocene, nearly the entire Oligocene, the Miocene from about 17 Ma, the entire Pliocene and much of the Pleistocene. The paleomagnetic properties are generally suitable for magnetostratigraphic interpretation, with well-behaved demagnetization diagrams, uniform distribution of declinations, and a clear separation into two inclination modes. Although the sequences were discontinuously recovered with many gaps due to coring, and there are hiatuses from sedimentary and tectonic processes, the magnetostratigraphic patterns are in general readily interpretable. Our interpretations are integrated with the diatom, radiolarian, calcareous nannofossils and dinoflagellate cyst (dinocyst) biostratigraphy. The magnetostratigraphy significantly improves the resolution of the chronostratigraphy, particularly in intervals with poor biostratigraphic control. However, Southern Ocean records with reliable magnetostratigraphies are notably scarce, and the data reported here provide an opportunity for improved calibration of the biostratigraphic records. In particular, we provide a rare magnetostratigraphic calibration for dinocyst biostratigraphy in the Paleogene and a substantially improved diatom calibration for the Pliocene. This paper presents the stratigraphic framework for future paleoceanographic proxy records which are being developed for the Wilkes Land margin cores. It further provides tight constraints on the duration of regional hiatuses inferred from seismic surveys of the region.

Abundance patterns and isotopic signals of morphotypes of Globigerinoides ruber

The chemical composition of shells of the planktonic foraminifer Globigerinoides ruber (white) is frequently used to determine past sea surface conditions. Recently, it has been shown that arbitrarily defined morphotypes within this species exhibit different chemical and isotopic signatures. Here, we investigate the occurrence through time and in space of morphological types of G. ruber (white) in late Quaternary and Holocene sediments of the central and the eastern Mediterranean Sea. In 115 samples representing two distinct time intervals (MIS 1-2 and MIS 9-12) at ODP Site 964 and the piston core GeoTü-SL96, we have defined three morphological types within this species and determined their relative abundances and stable isotopic composition. A quantitative analysis of morphological variation within G. ruber (white) in four samples revealed that the subjectively defined morphotypes occupy separate segments of a continuous and homogenous morphospace. We further show that the abundance of the morphotypes changes significantly between glacials and interglacials and that the three morphotypes of G. ruber show significant offsets in their stable isotopic composition. These offsets are consistent within glacial and interglacial stages but their sign is systematically reversed between the two Sites. Since the isotopic shifts among the three G. ruber morphotypes are systematic and often exceed 1per mil, their understanding is essential for the interpretation of all G. ruber-based proxy records for the paleoceanographic development of the Mediterranean during the late Quaternary.

Aplicación de Métodos Meshless al Análisis de Problemas de Autovalores

La presente Tesis Doctoral aborda la aplicación de métodos meshless, o métodos sin malla, a problemas de autovalores, fundamentalmente vibraciones libres y pandeo. En particular, el estudio se centra en aspectos tales como los procedimientos para la resolución numérica del problema de autovalores con estos métodos, el coste computacional y la viabilidad de la utilización de matrices de masa o matrices de rigidez geométrica no consistentes. Además, se acomete en detalle el análisis del error, con el objetivo de determinar sus principales fuentes y obtener claves que permitan la aceleración de la convergencia. Aunque en la actualidad existe una amplia variedad de métodos meshless en apariencia independientes entre sí, se han analizado las diferentes relaciones entre ellos, deduciéndose que el método Element-Free Galerkin Method [Método Galerkin Sin Elementos] (EFGM) es representativo de un amplio grupo de los mismos. Por ello se ha empleado como referencia en este análisis. Muchas de las fuentes de error de un método sin malla provienen de su algoritmo de interpolación o aproximación. En el caso del EFGM ese algoritmo es conocido como Moving Least Squares [Mínimos Cuadrados Móviles] (MLS), caso particular del Generalized Moving Least Squares [Mínimos Cuadrados Móviles Generalizados] (GMLS). La formulación de estos algoritmos indica que la precisión de los mismos se basa en los siguientes factores: orden de la base polinómica p(x), características de la función de peso w(x) y forma y tamaño del soporte de definición de esa función. Se ha analizado la contribución individual de cada factor mediante su reducción a un único parámetro cuantificable, así como las interacciones entre ellos tanto en distribuciones regulares de nodos como en irregulares. El estudio se extiende a una serie de problemas estructurales uni y bidimensionales de referencia, y tiene en cuenta el error no sólo en el cálculo de autovalores (frecuencias propias o carga de pandeo, según el caso), sino también en términos de autovectores. This Doctoral Thesis deals with the application of meshless methods to eigenvalue problems, particularly free vibrations and buckling. The analysis is focused on aspects such as the numerical solving of the problem, computational cost and the feasibility of the use of non-consistent mass or geometric stiffness matrices. Furthermore, the analysis of the error is also considered, with the aim of identifying its main sources and obtaining the key factors that enable a faster convergence of a given problem. Although currently a wide variety of apparently independent meshless methods can be found in the literature, the relationships among them have been analyzed. The outcome of this assessment is that all those methods can be grouped in only a limited amount of categories, and that the Element-Free Galerkin Method (EFGM) is representative of the most important one. Therefore, the EFGM has been selected as a reference for the numerical analyses. Many of the error sources of a meshless method are contributed by its interpolation/approximation algorithm. In the EFGM, such algorithm is known as Moving Least Squares (MLS), a particular case of the Generalized Moving Least Squares (GMLS). The accuracy of the MLS is based on the following factors: order of the polynomial basis p(x), features of the weight function w(x), and shape and size of the support domain of this weight function. The individual contribution of each of these factors, along with the interactions among them, has been studied in both regular and irregular arrangement of nodes, by means of a reduction of each contribution to a one single quantifiable parameter. This assessment is applied to a range of both one- and two-dimensional benchmarking cases, and includes not only the error in terms of eigenvalues (natural frequencies or buckling load), but also of eigenvectors

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

The scenario of two-dimensional instabilities of the cylinder wake under EHD forcing: A linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point. Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary. In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies. After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared.