Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

Effect of wave frequency on the nonlinear interaction between Görtler vortices and three-dimensional Tollmien-Schlichting waves

The nonlinear interaction between Görtler vortices (GV) and three-dimensional Tollmien-Schlichting (TS) waves nonlinear interaction is studied with a spatial, nonparallel model based on the Parabolized Stability Equations (PSE). In this investigation the effect of TS wave frequency on the nonlinear interaction is studied. As verified in previous investigations using the same numerical model, the relative amplitudes and growth rates are the dominant parameters in GV/TS wave interaction. In this sense, the wave frequency influence is important in defining the streamwise distance traveled by the disturbances in the unstable region of the stability diagram and in defining the amplification rates that they go through.

Microcracks and Vortices in Superconducting Thin Films

In this work, superconducting YBa₂ Cu₃O_6+x (YBCO) thin films have been studied with the experimental focus on the anisotropy of BaZrO₃ (BZO) doped YBCOthin films and the theoretical focus on modelling flux pinning by numerically solving Ginzburg- Landau equations. Also, the structural properties of undoped YBCO thin films grown on NdGaO₃ (NGO) and MgO substrates were investigated. The thin film samples were made by pulsed laser ablation on single crystal substrates. The structural properties of the thin films were characterized by X-ray diffraction and atomic force microscope measurements. The superconducting properties were investigated with a magnetometer and also with transport measurements in pulsed magnetic field up to 30 T. Flux pinning was modelled by restricting the value of the order parameter inside the columnar pinning sites and then solving the Ginzburg-Landau equations numerically with the restrictions in place. The computations were done with a parallel code on a supercomputer. The YBCO thin films were seen to develop microcracks when grown on NGO or MgO substrates. The microcrack formation was connected to the structure of the YBCO thin films in both cases. Additionally, the microcracks can be avoided by careful optimization of the deposition parameters and the film thickness. The BZO doping of the YBCO thin films was seen to decrease the effective electron mass anisotropy, which was seen by fitting the Blatter scaling to the angle dependence of the upper critical field. The Ginzburg-Landau simulations were able to reproduce the measured magnetic field dependence of the critical current density for BZO doped and undoped YBCO. The simulations showed that in addition to the large density also the large size of the BZO nanorods is a key factor behind the change in the power law behaviour between BZO doped and undoped YBCO. Additionally, the Ginzburg-Landau equations were solved for type I thin films where giant vortices were seen to appear depending on the film thickness. The simulations predicted that singly quantized vortices are stable in type I films up to quite large thicknesses and that the size of the vortices increases with decreasing film thickness, in a way that is similar to the behaviour of the interaction length of Pearl vortices.

Interaction between vortices and impurities in a d-wave superconductor /

High temperature superconductors were discovered in 1986, but despite considerable research efforts, both experimental and theoretical, these materials remain poorly understood. Because their electronic structure is both inhomogeneous and highly correlated, a full understanding will require knowledge of quasiparticle properties both in real space and momentum space. In this thesis, we will present a theoretical analysis of the scanning tunneling microscopy (STM) data in BSCCO. We introduce the Bogoliubov-De Gennes Hamiltonian and solve it numerically on a two-dimensional 20 x 20 lattice under a magnetic field perpendicular to the surface. We consider a vortex at the center of our model. We introduce a Zn impurity in our lattice as a microscopic probe of the physical properties of BSCCO. By direct numerical diagonalization of the lattice BogoliubovDe Gennes Hamiltonian for different positions of the impurity, we can calculate the interaction between the vortex and the impurity in a d-wave superconductor.

Doppler vortography : detection and quantification of the vortices in the left ventricle

Nous proposons une nouvelle méthode pour quantifier la vorticité intracardiaque (vortographie Doppler), basée sur l’imagerie Doppler conventionnelle. Afin de caractériser les vortex, nous utilisons un indice dénommé « Blood Vortex Signature (BVS) » (Signature Tourbillonnaire Sanguine) obtenu par l’application d’un filtre par noyau basé sur la covariance. La validation de l’indice BVS mesuré par vortographie Doppler a été réalisée à partir de champs Doppler issus de simulations et d’expériences in vitro. Des résultats préliminaires obtenus chez des sujets sains et des patients atteints de complications cardiaques sont également présentés dans ce mémoire. Des corrélations significatives ont été observées entre la vorticité estimée par vortographie Doppler et la méthode de référence (in silico: r2 = 0.98, in vitro: r2 = 0.86). Nos résultats suggèrent que la vortographie Doppler est une technique d’échographie cardiaque prometteuse pour quantifier les vortex intracardiaques. Cet outil d’évaluation pourrait être aisément appliqué en routine clinique pour détecter la présence d’une insuffisance ventriculaire et évaluer la fonction diastolique par échocardiographie Doppler.

Perturbed Rankine vortices in surface quasi-geostrophic dynamics

An analytical dispersion relation is derived for linear perturbations to a Rankine vortex governed by surface quasi-geostrophic dynamics. Such a Rankine vortex is a circular region of uniform anomalous surface temperature evolving under quasi-geostrophic dynamics with uniform interior potential vorticity. The dispersion relation is analysed in detail and compared to the more familiar dispersion relation for a perturbed Rankine vortex governed by the Euler equations. The results are successfully verified against numerical simulations of the full equations. The dispersion relation is relevant to problems including wave propagation on surface temperature fronts and the stability of vortices in quasi-geostrophic turbulence.

Characterising the variability and extremes of the stratospheric polar vortices using 2D moment analysis

The mean state, variability and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere vortex, are examined using 2-dimensional moment analysis and Extreme Value Theory (EVT). The use of moments as an analysis to ol gives rise to information about the vortex area, centroid latitude, aspect ratio and kurtosis. The application of EVT to these moment derived quantaties allows the extreme variability of the vortex to be assessed. The data used for this study is ECMWF ERA-40 potential vorticity fields on interpolated isentropic surfaces that range from 450K-1450K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850K (∼10hPa) surface over the 1958-2001 period are fitted with parametric distributions, and show that SSW events comprise the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere, and shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern Hemisphere (NH) and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, and confirm that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally extreme value theory is used to statistically mo del the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

The nature of Arctic polar vortices in chemistry-climate models

The structure of the Arctic stratospheric polar vortex in three chemistry–climate models (CCMs) taken from the CCMVal-2 intercomparison is examined using zonal mean and geometric-based methods. The geometric methods are employed by taking 2D moments of potential vorticity fields that are representative of the polar vortices in each of the models. This allows the vortex area, centroid location and ellipticity to be determined, as well as a measure of vortex filamentation. The first part of the study uses these diagnostics to examine how well the mean state, variability and extreme variability of the polar vortices are represented in CCMs compared to ERA-40 reanalysis data, and in particular for the UMUKCA-METO, NIWA-SOCOL and CCSR/NIES models. The second part of the study assesses how the vortices are predicted to change in terms of the frequency of sudden stratospheric warmings and their general structure over the period 1960–2100. In general, it is found that the vortices are climatologically too far poleward in the CCMs and produce too few large-scale filamentation events. Only a small increase is observed in the frequency of sudden stratospheric warming events from the mean of the CCMVal-2 models, but the distribution of extreme variability throughout the winter period is shown to change towards the end of the twentyfirst century.

Hurricane-type vortices in a general circulation model

A very high resolution atmospheric general circulation model, T106-L19, has been used for the simulation of hurricanes in a multi-year numerical experiment. Individual storms as well as their geographical and seasonal distribution agree remarkably well with observations. In spite of the fact that only the thermal and dynamical structure of the storms have been used as criteria of their identification, practically all of them occur in areas where the sea surface temperature is higher or equal to 26 °C. There are considerable variations from year to year in the number of storms in spite of the fact that there are no interannual variations in the SST pattern. It is found that the number of storms in particular areas appear to depend on the intensity of the Hadley-Walker cell. The result is clearly resolution-dependant. At lower horizonal resolution, T42, for example, the intensity of the storms is significantly reduced and their overall structure is less realistic, including their vertical form and extent.

Simulation of hurricane-type vortices in a general circulation model

A study of intense hurricane-type vortices in the ECMWF operational model is reported. These vortices develop around day 4 in the forecast and occur in the tropical belt in areas and at times where intense tropical cyclones normally occur. The frequency resembles that observed over most tropical regions with a pronounced maximum in the western North Pacific. The life time of the vortices and their 3-dimensional structure agree in some fundamental way with observations although, because of the resolution, the systems are less intense than the observed ones. The general large-scale conditions for active and inactive cyclone periods are discussed. The model cyclones are sensitive to the sea-surface temperature and do not develop with sea surface temperatures lower than 28–29°C. The dynamical conditions favouring cyclone development are characterized by intense large-scale divergence in the upper troposphere. Cyclogenesis appears to take place when these conditions are found outside the equatorial zone and over oceans where the water is sufficiently warm.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.