Large-scale flow in a cubic Rayleigh-Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions. - In: Philosophical transactions of the Royal Society, ISSN 1471-2962, Bd. 380 (2022), 2225, 20210042, S. 1-18
We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times.
https://doi.org/10.1098/rsta.2021.0042
Collapse of coherent large scale flow in strongly turbulent liquid metal convection. - In: Physical review letters, ISSN 1079-7114, Bd. 128 (2022), 16, S. 164501-1-164501-6
https://doi.org/10.1103/PhysRevLett.128.164501
Embedding classical dynamics in a quantum computer. - In: Physical review, ISSN 2469-9934, Bd. 105 (2022), 5, 052404, insges. 47 S.
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides an operator-theoretic representation of classical dynamics by combining ergodic theory with quantum information science. The resulting quantum embedding of classical dynamics (QECD) enables efficient simulation of spaces of classical observables with exponentially large dimension using a quadratic number of quantum gates. The QECD framework is based on a quantum feature map that we introduce for representing classical states by density operators on a reproducing kernel Hilbert space, H. Furthermore, an embedding of classical observables into self-adjoint operators on H is established, such that quantum mechanical expectation values are consistent with pointwise function evaluation. In this scheme, quantum states and observables evolve unitarily under the lifted action of Koopman evolution operators of the classical system. Moreover, by virtue of the reproducing property of H, the quantum system is pointwise-consistent with the underlying classical dynamics. To achieve a quantum computational advantage, we project the state of the quantum system onto a finite-rank density operator on a 2n-dimensional tensor product Hilbert space associated with n qubits. By employing discrete Fourier-Walsh transforms of spectral functions, the evolution operator of the finite-dimensional quantum system is factorized into tensor product form, enabling implementation through an n-channel quantum circuit of size O(n) and no interchannel communication. Furthermore, the circuit features a state preparation stage, also of size O(n), and a quantum Fourier transform stage of size O(n2), which makes predictions of observables possible by measurement in the standard computational basis. We prove theoretical convergence results for these predictions in the large-qubit limit, n&flech;∞. In light of these properties, QECD provides a consistent simulator of the evolution of classical observables, realized through projective quantum measurement, which is able to simulate spaces of classical observables of dimension 2n using circuits of size O(n2). We demonstrate the consistency of the scheme in prototypical dynamical systems involving periodic and quasiperiodic oscillators on tori. These examples include simulated quantum circuit experiments in Qiskit Aer, as well as actual experiments on the IBM Quantum System One.
https://doi.org/10.1103/PhysRevA.105.052404
Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection. - In: Physics of fluids, ISSN 1089-7666, Bd. 34 (2022), 4, 045106, S. 045106-1-045106-14
A combined convolutional autoencoder-recurrent neural network machine learning model is presented to directly analyze and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-Bénard convection flow at Prandtl number Pr=7 and Rayleigh number Ra=10^7. Two recurrent neural networks are applied for the temporal advancement of turbulent heat transfer data in the reduced latent data space, an echo state network, and a recurrent gated unit. Thereby, our work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework. This suggests that the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to coarse grids of larger-scale computational models, such as global circulation models for atmosphere and ocean.
https://doi.org/10.1063/5.0087977
Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows. - In: Chaos, ISSN 1089-7682, Bd. 32 (2022), 1, 013123, S. 013123-1-013123-11
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.
https://doi.org/10.1063/5.0076035
Rayleigh-Bénard convection in air: out-of-plane vorticity from stereoscopic PIV measurements. - In: International Symposium on Particle Image Velocimetry, ISSN 2769-7576, Bd. 1 (2021), 1, insges. 2 S.
https://doi.org/10.18409/ispiv.v1i1.44
Non-Boussinesq convection at low Prandtl numbers relevant to the Sun. - In: Physical review fluids, ISSN 2469-990X, Bd. 6 (2021), 10, 100503, S. 100503-1-100503-19
https://doi.org/10.1103/PhysRevFluids.6.100503
The von Kármán Vortex Street, an archetype for Machine Learning in turbulence. - In: Experimentelle Strömungsmechanik - 28. Fachtagung, 7.-9. September 2021, Bremen, (2021), 29
Transformation of a submerged flat jet under strong transverse magnetic field. - In: epl, ISSN 1286-4854, Bd. 134 (2021), 2, S. 24003-p1-24003-p7
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.
https://doi.org/10.1209/0295-5075/134/24003
Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow(a). - In: epl, ISSN 1286-4854, Bd. 134 (2021), 3, S. 34004-p1-34004-p7
We study the connection between extreme events of thermal and kinetic energy dissipation rates in the bulk of three-dimensional Rayleigh-Bénard convection and the wall shear stress patterns at the top and the bottom plates that enclose the layer. Zero points of this two-dimensional vector field stand for detachments of strong thermal plumes. If their position at the opposite plates and a given time is close then they can be considered as precursors for high-amplitude bulk dissipation events triggered by plume collisions or close passings. This scenario requires a breaking of the synchronicity of the boundary layer dynamics at both plates which is found to be in line with a transition of the bulk derivative statistics from Gaussian to intermittent. Our studies are based on three-dimensional high-resolution direct numerical simulations for moderate Rayleigh numbers between and .
https://doi.org/10.1209/0295-5075/134/34004