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Pushenko, Vladyslav; Schumacher, Jörg
Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow. - In: Physical review, ISSN 2470-0053, Bd. 109 (2024), 4, 045101

The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equations of water vapor mixing ratio and temperature to an effective advection-diffusion equation for the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ1 ≥ λ2 ≥ λ3 are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ3 < 0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ3 and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.
Vieweg, Philipp; Klünker, Anna; Schumacher, Jörg; Padberg-Gehle, Kathrin
Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection. - In: European journal of mechanics, ISSN 1873-7390, Bd. 103 (2024), S. 69-85

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.
Vieweg, Philipp;
Supergranule aggregation: a Prandtl number-independent feature of constant heat flux-driven convection flows. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 980 (2024), A46, S. A46-1-A46-13

Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh-Bénard convection at a fixed Rayleigh number Ra ≈ 2.0 × 10^^ 5 across 4 orders of Prandtl numbers Pr ∈ [10^−2, 10^2] by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio Γ = 60. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of Pr on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.
Chu, Xu; Pandey, Sandeep
Non-intrusive, transferable model for coupled turbulent channel-porous media flow based upon neural networks. - In: Physics of fluids, ISSN 1089-7666, Bd. 36 (2024), 2, 025112, S. 025112-1-025112-13

Turbulent flow over permeable interfaces is omnipresent featuring complex flow topology. In this work, a data-driven, end-to-end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have derived a non-linear reduced order model (ROM) with a deep convolution autoencoder. This model can reduce highly resolved spatial dimensions, which is a prerequisite for direct numerical simulation, by 99%. A downstream recurrent neural network has been trained to capture the temporal trend of reduced modes; thus, it is able to provide future evolution of modes. We further evaluate the trained model's capability on a newer dataset with a different porosity. In such cases, fine-tuning could reduce the efforts (up to two-order of magnitude) to train a model with limited dataset (10%) and knowledge and still show a good agreement on the mean velocity profile. Especially, the fine-tuned model shows a better agreement in the porous domain than the channel and interface areas indicating the topological feature is less challenging for training than the multi-scale nature of the turbulent flows. Leveraging the current model, we find that even quick fine-tuning achieves an impressive order-of-magnitude reduction in training time by approximately O(102) and still results in effective flow predictions. This promising discovery encourages the fast development of a substantial amount of data-driven models tailored for various types of porous media. The diminished training time substantially lowers the computational cost when dealing with changing porous topologies, making it feasible to systematically explore interface engineering with different types of porous media.
Bhattacharya, Shashwat; Boeck, Thomas; Krasnov, Dmitry; Schumacher, Jörg
Wall-attached convection under strong inclined magnetic fields. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 979 (2024), A53, S. A53-1-A53-27

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of a homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The aforementioned results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection. The direct numerical simulation results also reveal that at least for large values of horizontal magnetic field, the wall-mode structures and the resulting heat transfer are dependent on the initial conditions.
Belyaev, Ivan A.; Chernysh, Denis Yu.; Luchinkin, Nikita A.; Krasnov, Dmitry; Kolesnikov, Yuri; Listratov, Yaroslav I.
Formation of the inlet flow profile for passive control of a magnetohydrodynamic liquid-metal flow in a channel. - In: High temperature, ISSN 1608-3156, Bd. 61 (2023), 3, S. 417-428

The paper describes an experimental attempt to affect the flow of liquid metal using a relatively small perturbation at an inlet to a long channel. The purpose is to form a flow structure which is stable in a strong magnetic field at high heat loads, enhance heat transfer, and achieve more predictable flow parameters. It is demonstrated that an obstacle in the form of a rod located transverse to the flow and parallel to the applied magnetic field and installed at the inlet can induce perturbations in the form of regular vortices observed along the flow at lengths as great as several tens of channel hydraulic diameters. The experiments confirm that thus generated vortices considerably change the structure of the isothermal MHD flow. In the case of mixed convection, such vortices suppress the development large-scale thermogravitational fluctuations in the flow and enhance heat transfer under certain flow conditions.
Jansson, Niclas; Karp, Martin; Perez, Adalberto; Mukha, Timofey; Ju, Yi; Liu, Jiahui; Páll, Szilárd; Laure, Erwin; Weinkauf, Tino; Schumacher, Jörg; Schlatter, Philipp; Markidis, Stefano
Exploring the ultimate regime of turbulent Rayleigh-Bénard Convection through unprecedented spectral-element simulations. - In: SC '23: proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, (2023), 5, S. 1-9

We detail our developments in the high-fidelity spectral-element code Neko that are essential for unprecedented large-scale direct numerical simulations of fully developed turbulence. Major innovations are modular multi-backend design enabling performance portability across a wide range of GPUs and CPUs, a GPU-optimized preconditioner with task overlapping for the pressure-Poisson equation and in-situ data compression. We carry out initial runs of Rayleigh-Bénard Convection (RBC) at extreme scale on the LUMI and Leonardo supercomputers. We show how Neko is able to strongly scale to 16,384 GPUs and obtain results that are not possible without careful consideration and optimization of the entire simulation workflow. These developments in Neko will help resolving the long-standing question regarding the ultimate regime in RBC.
Vieweg, Philipp;
Large-scale flow structures in turbulent Rayleigh-Bénard convection: dynamical origin, formation, and role in material transport. - Ilmenau : Universitätsbibliothek, 2023. - 1 Online-Ressource (xiv, 134 Seiten)
Technische Universität Ilmenau, Dissertation 2023

Thermische Konvektion ist der essentielle Mechanismus durch welchen Wärme in vielen natürlichen Strömungen übertragen wird und weist zugleich oftmals eine Hierarchie von verschiedenen Strömungsstrukturen auf. Jedes Umfeld kann dabei über seine eigenen charakteristischen Randbedingungen verfügen, wobei die solare Konvektionszone das wohl bekannteste Beispiel mit ausgeprägter Strukturhierarchie repräsentiert. Die Entstehung Letzterer und die Rolle der involvierten Strömungsmuster bzgl. des materiellen Transports stellen wichtige offene Fragen der Wissenschaft dar. Die vorliegende Arbeit (1) erweitert unser Verständnis von der Beeinflussung großskaliger Strömungsstrukturen durch verschiedene Randbedingungen und (2) untersucht diese Muster aus der Perspektive materiellen Transports. Zu diesem Zweck wird Rayleigh-Bénard Konvektion - ein Paradigma natürlicher thermischer Konvektion - mittels direkter numerischer Simulationen untersucht. Das erste wesentliche Ergebnis wird durch eine explorative Studie verschiedener idealisierter mechanischer und thermischer Randbedingungen erreicht. Es wird gezeigt, dass Letztere die Natur der großskaligen Strömungsstrukturen fundamental bestimmen. Wird eine konstante Wärmestromdichte aufgeprägt, so kann eine allmähliche Aggregation kleinerer Konvektionszellen zu einer die gesamte Domäne füllenden Konvektionsstruktur - welche in Analogie zur astrophysikalischen Motivation als Supergranule bezeichnet wird - für alle zugänglichen Rayleigh- und Prandtl-Zahlen beobachtet werden. Es wird zudem gezeigt, dass schwache Rotation um die vertikale Achse imstande ist, den Aggregationsprozess zu beschränken. Der dynamische Ursprung und die Formierung der Supergranulen werden im Kontext von Instabilitäten und spektralen Kaskaden analysiert. Das zweite wesentliche Ergebnis wird durch die Analyse der Entwicklung von masselosen Lagrange'schen Partikeln im klassischen, durch konstante Temperaturen angetriebenen Szenario erzielt. Unüberwachtes maschinelles Lernen wird dazu benutzt, kohärente Regionen zu identifizieren, welche anschließend mit den großskaligen Strömungsstrukturen in Verbindung gebracht und bzgl. ihres Wärmetransportes in verschiedenen Fluiden analysiert werden. Abschließend wird eine neue evolutionäre Clustering-Methode entwickelt, welche künftig auf die Supergranulenaggregation angewendet werden kann. Diese Arbeit beschreibt einen neuen Mechanismus der Selbstorganisation von Strömungen und erweitert damit unser Verständnis großskaliger Strömungsstrukturen thermischer Konvektion. Die Einfachheit des untersuchten dynamischen Systems erlaubt eine Übertragung auf verschiedenste natürliche Strömungen sowie deren erfolgreichere Interpretation.
Sharifi Ghazijahani, Mohammad; Heyder, Florian; Schumacher, Jörg; Cierpka, Christian
Spatial prediction of the turbulent unsteady von Kármán vortex street using echo state networks. - In: Physics of fluids, ISSN 1089-7666, Bd. 35 (2023), 11, 115141, S. 115141-1-115141-15

The spatial prediction of the turbulent flow of the unsteady von Kármán vortex street behind a cylinder at Re = 1000 is studied. For this, an echo state network (ESN) with 6000 neurons was trained on the raw, low-spatial resolution data from particle image velocimetry. During prediction, the ESN is provided one half of the spatial domain of the fluid flow. The task is to infer the missing other half. Four different decompositions termed forward, backward, forward-backward, and vertical were examined to show whether there exists a favorable region of the flow for which the ESN performs best. Also, it was checked whether the flow direction has an influence on the network's performance. In order to measure the quality of the predictions, we choose the vertical velocity prediction of direction (VVPD). Furthermore, the ESN's two main hyperparameters, leaking rate (LR) and spectral radius (SR), were optimized according to the VVPD values of the corresponding network output. Moreover, each hyperparameter combination was run for 24 random reservoir realizations. Our results show that VVPD values are highest for LR ≈ 0.6, and quite independent of SR values for all four prediction approaches. Furthermore, maximum VVPD values of ≈ 0.83 were achieved for backward, forward-backward, and vertical predictions while for the forward case VVPDmax = 0.74 was achieved. We found that the predicted vertical velocity fields predominantly align with their respective ground truth. The best overall accordance was found for backward and forward-backward scenarios. In summary, we conclude that the stable quality of the reconstructed fields over a long period of time, along with the simplicity of the machine learning algorithm (ESN), which relied on coarse experimental data only, demonstrates the viability of spatial prediction as a suitable method for machine learning application in turbulence.
Pfeffer, Philipp; Heyder, Florian; Schumacher, Jörg
Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing. - In: Physical review research, ISSN 2643-1564, Bd. 5 (2023), 4, 043242, S. 043242-1-043242-13

Two hybrid quantum-classical reservoir computing models are presented to reproduce the low-order statistical properties of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number Ra=105 and Prandtl number Pr=10. These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. The latter is composed of vertical velocity and temperature and measures the global turbulent heat transfer across the convection layer; it manifests locally in coherent hot and cold thermal plumes that rise from the bottom and fall from the top boundaries. Both quantum algorithms differ by the arrangement of the circuit layers of the quantum reservoir, in particular the entanglement layers. The second of the two quantum circuit architectures, denoted H2, enables a complete execution of the reservoir update inside the quantum circuit without the usage of external memory. Their performance is compared with that of a classical reservoir computing model. Therefore, all three models have to learn the nonlinear and chaotic dynamics of the turbulent flow at hand in a lower-dimensional latent data space which is spanned by the time-dependent expansion coefficients of the 16 most energetic proper orthogonal decomposition (POD) modes. These training data are generated by a POD snapshot analysis from direct numerical simulations of the original turbulent flow. All reservoir computing models are operated in the reconstruction or open-loop mode, i.e., they receive three POD modes as an input at each step and reconstruct the 13 missing modes. We analyze different measures of the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared with the classical reservoir network. Most importantly, the quantum reservoirs are by a factor of four to eight smaller in comparison with the classical case.