Publications

The impact of variable material properties, such as temperature-dependent thermal conductivity and dynamical viscosity, on the dynamics of a fully compressible turbulent convection flow beyond the anelastic limit is studied in the present work by two series of three-dimensional direct numerical simulations in a layer of aspect ratio 4 with periodic boundary conditions in both horizontal directions. One simulation series is for a weakly stratified adiabatic background and the other one for a strongly stratified one. The Rayleigh number is 10^5 and the Prandtl number is 0.7 throughout this study. The temperature dependence of material parameters is imposed as a power law with an exponent β. It generates a superadiabaticity ε (z) that varies across the convection layer. Central statistical quantities of the flow, such as the mean superadiabatic temperature, temperature and density fluctuations, or turbulent Mach numbers are compared in the form of horizontal plane-time averaged profiles. It is found that the additional material parameter dependence causes systematic quantitative changes of all these quantities, but no qualitative ones. A growing temperature power law exponent β also enhances the turbulent momentum transfer in the weak stratification case by 40%, and it reduces the turbulent heat transfer by up to 50% in the strong stratification case.

Magnetoconvection in a tall vertical box with vertical hot and cold walls, and an imposed steady uniform magnetic field perpendicular to the temperature gradient, is analyzed numerically. The geometry and the values of the non-dimensional parameters - the Prandtl number of 0.025, the Rayleigh number of 7.5×10^5, and the Hartmann number between 0 and 798 - match those of an earlier experiment. A parametric study of the effect of wall electric conductivity, across a wide range of conductance ratio values, on flow properties is performed. Two configurations of electric boundary conditions are explored. In one configuration, all walls have finite electric conductivity, while in the other, only the walls with constant temperature are electrically conducting. The flows are analyzed using their integral properties and distributions of velocity, temperature, and electric currents. It is found that, in general, the convection flow is suppressed by the magnetic field. However, this effect is strongly modified by the wall’s electric conductivity and is markedly different for the two wall configurations. The associated changes in flow structure, rate of heat transfer, and flow’s kinetic energy are revealed. It is also shown that the assumption of quasi-two-dimensionality may not be valid under some conditions, even at high Hartmann numbers.

The effect of an imposed magnetic field on the flow of an electrically conducting fluid in a channel geometry is investigated numerically using high-performance temporal simulations. For the strongest spanwise magnetic fields considered, the turbulent state appears metastable, which makes the determination of the associated tipping point arduous. As an alternative, edge states, i.e., unstable states located on the state space boundary between the laminar and the turbulent basin of attraction, are investigated in detail. Their continuation smoothly leads to the tipping point where they are expected to collide with the turbulent dynamics. As the magnetic field intensity is raised, edge states become, on average, more energetic and more unstable, while their fluctuations become more chaotic, less predictable, and less symmetric. Nevertheless, their continuation allows one to accurately determine the value of the tipping point beyond which the laminar state becomes the only attractor.

In dieser Arbeit wird das Potenzial von Machine-Learning-Algorithmen (ML) zur Verbesserung der Parametrisierung von großskaligen atmosphärischen Simulationen untersucht. Herkömmliche Ansätze verwenden oft Vereinfachungen oder rechenintensive Methoden. Diese Arbeit beabsichtigt, einen physikalisch konsistenten und rechnerisch effizienten Ansatz einzuführen, der Reservoir Computing (RC) und Datenkompression nutzt, um subgitter-skalige Merkmale aus direkten numerischen Simulationen (DNS) der thermischen Konvektion zu extrahieren. Hierbei wird der hochaufgelöste Simulationsdatensatz zuerst durch Proper Orthogonal Decomposition (POD) oder ein Autoencoder-Netzwerk (AE) vorverarbeitet, um die Datenmenge zu reduzieren. Anschließend wird ein RC-Modell auf diesem reduzierten Datenraum trainiert, um zukünftige Strömungszustände ohne die Lösung der nichtlinearen Bewegungsgleichungen vorherzusagen. Die Vorhersagen des kombinierten POD-RC-Modells werden anhand der Originalsimulationen validiert. Das Modell reproduziert die strukturellen und statistischen Merkmale von trockenen und feuchten Konvektionsströmungen und eröffnet somit neue Wege für die dynamische Parametrisierung des subgrid-skaligen Transports in grob aufgelösten Zirkulationsmodellen. Des Weiteren untersucht die Studie die Verallgemeinerungseigenschaften eines AE-RC-Modells basierend auf einem wärmeflussgetriebenen zweidimensionalen turbulenten Konvektionssystem. Dabei zeigt sich, dass das AE-RC-Modell die räumliche Struktur und statistischen Eigenschaften der ungesehenen physikalischen Felder korrekt wiedergibt. Schließlich liegt der Fokus auf der Parametrisierung der konvektiven Grenzschicht (CBL) mithilfe eines Generative Adversarial Networks (GAN), das auf hochaufgelösten DNS-Daten einer dreidimensionalen CBL trainiert wird. Es wird gezeigt, dass die Methode durch eine physikalisch informierte Reskalierung der begrenzten Trainingsdaten in der Lage ist, das CBL-Wachstum und die damit verbundene Musterbildung zu reproduzieren. Die GAN-Ergebnisse stimmen mit Standard Mass-Flux Parametrisierungen überein und liefern zusätzlich die horizontale Anordnung der turbulenten Strömung, die mit dem Mass-Flux-Ansatz nicht erreicht werden kann. Obwohl die Implementierung von ML-basierten Parametrisierungsschemata in großskaligen Modellen nicht im Fokus steht, trägt diese Arbeit dazu bei, unser Verständnis des Potenzials und der Grenzen dieser Modelle im Kontext der Klimamodellierung und numerischen Wettervorhersage zu vertiefen.

We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-Bénard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Second, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.