Publikationen

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes.

A duct flow generated by a planar jet at the inlet and affected by a magnetic field perpendicular to the jet's plane is analyzed in high-resolution numerical simulations. The case of very high Reynolds and Hartmann numbers is considered. It is found that the flow structure is drastically modified in the inlet area. It becomes determined by three new planar jets oriented along the magnetic field lines: two near the walls and one in the middle of the duct. The downstream evolution of the flow includes the Kelvin-Helmholtz instability of the jets and slow decay of the resulting quasi-two-dimensional turbulence.

A liquid metal flat jet immersed in a square duct under the influence of a transverse magnetic field is studied experimentally. Two cases are considered: when the applied magnetic field is oriented parallel (coplanar field) or perpendicularly (transverse field) to the initial plane of the jet. The main goal of the study is to investigate the mean flow characteristics and the stages of the jet's transformation. Signals of streamwise velocity at different locations are measured, which allows us to determine average velocity profiles and spatial-temporal characteristics of the velocity field. The two considered configurations are directly compared under the same flow regimes, with the same equipment.

Recurrent neural networks are machine learning algorithms that are well suited to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations to obtain training and test data for the algorithm. Both sets are preprocessed by a proper orthogonal decomposition (POD) using the snapshot method to reduce the amount of data. Training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by these data and predicts future flow states. The predictions are thoroughly validated by original simulations. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.