Publikationen

In an attempt to understand the role of the strong radial dependence of thermal diffusivity on the properties of convection in Sun-like stars, we mimic that effect in non-Oberbeck-Boussinesq convection in a horizontally extended rectangular domain (aspect ratio 16) by allowing the thermal diffusivity to increase with the temperature (as in the case of stars). Direct numerical simulations (i.e., numerical solutions of the governing equations by resolving up to the smallest scales without requiring any modeling) show that, in comparison with Oberbeck-Boussinesq simulations (two of which we perform for comparison purposes), the symmetry of the temperature field about the mid-horizontal plane is broken, whereas the velocity and heat flux profiles remain essentially symmetric. Our choice of (T), which resembles the variation in stars, results in a temperature field that loses its fine structures toward the hotter part of the computational domain, but the characteristic large scale of the turbulent thermal superstructures, which are structures whose size is typically larger than the depth of the convection domain, continues to be largely independent of the depth.

A pendulum with an attached permanent magnet moving near a conductor is a typical experiment for the demonstration of electromagnetic braking. When the conductor itself moves, it can transfer energy to the pendulum. We study a simple but exact analytical model where the conductor is a horizontally unbounded flat plate. For this geometry, eddy currents and induced Lorentz force due to the motion of a magnetic dipole are known analytically in the quasistatic limit. A vertical oscillation of such a horizontal plate located beneath the magnet is considered. In this setup, the vertical position of the pendulum is an equilibrium point when the magnetic moment of the magnet is perpendicular to its plane of motion. Depending on the strength of the magnetic dipole moment, the frequency and amplitude of the plate as well as the distance between plate and magnet, the plate oscillation can destabilize the equilibrium. The stability limits for weak electromagnetic coupling are computed analytically using the harmonic balancing method. For stronger coupling, the stability limits are obtained numerically using Floquet analysis. Chaotic motions with finite amplitudes are also found.

This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular vessel. The rectangular magnet provides a spatially non-uniform magnetic field that is known analytically. The magnet oscillation creates a steady mean flow (steady streaming) similar to those observed from oscillating rigid bodies. In the optimization problem, randomly distributed mass-less particles are advected by the flow to achieve a homogeneous distribution (objective function 1) while keeping the work done to move the permanent magnet minimal (objective function 2). A single evaluation of these two objective functions may take more than two hours. For that reason, to save computational time, the proposed method uses interpolation models on trust-regions for finding descent directions. We show that, even for our significantly simplified model problem, the mixing patterns vary significantly with the control parameters, which justifies the use of improved optimization techniques and their further development.

The article is devoted to an experimental study of a submerged flat jet flow in a transverse magnetic field. Two different approaches to the experimental study of jet flows are described. Detailed information about the experimental program and measuring methods presented here. The flow of a flat jet 6 mm high in a square channel with a side of 56 mm is considered. The channel is positioned so that the plane of the jet is perpendicular to the magnetic field induction. The results of measuring velocity profiles and waveforms by swivel-type probe with potential sensor are presented. Effects that can be interpreted in different ways are found: strongly unstationary flow regimes, mean flow reorganization, and development of near-wall jets. Additional experiments are prepared to obtain more detailed information about the restructuring and development of the jet. In particular, continuous measurements along the channel will be made in the presence of a slight main flow.

Reservoir computing is an efficient implementation of a recurrent neural network that can describe the evolution of a dynamical system by supervised machine learning with- out solving the underlying mathematical equations. In this work, reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number Ra = 10^7 and a Prandtl number Pr = 7 in an extended spatial domain with an aspect ratio of 6. Our data-driven approach, which is based on a long-term direct numerical simulation of the convection flow, comprises a two-step procedure: (1) reduction of the original simulation data by a proper orthogonal decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes which are associated with the largest total energy amplitudes; (2) setup and optimization of a reservoir computing model to describe the dynamical evolution of these 150 degrees of freedom and thus the large-scale evolution of the convection flow. The quality of the prediction of the reservoir computing model is comprehensively tested by a direct comparison of the results of the original direct numerical simulations and the fields that are reconstructed by means of the POD modes. We find a good agreement of the vertical profiles of mean temperature, mean convective heat flux, and root-mean-square temperature fluctuations. In addition, we discuss temperature variance spectra and joint probability density functions of the turbulent vertical velocity component and temperature fluctuation, the latter of which is essential for the turbulent heat transport across the layer. At the core of the model is the reservoir, a very large sparse random network characterized by the spectral radius of the corresponding adjacency matrix and a few further hyperparameters which are varied to investigate the quality of the prediction. Our work demonstrates that the reservoir computing model is capable of modeling the large-scale structure and low-order statistics of turbulent convection, which can open new avenues for modeling mesoscale convection processes in larger circulation models.