Publikationsliste (ERC)
 

  1. Pauluis and Schumacher, 2011, Self-aggregation of clouds in conditionally unstable moist convection, PNAS 108, 12623-12628
  2. Chillà and Schumacher, 2012, New perspectives in turbulent Rayleigh-Bénard convection, Eur. J. Phys. E 35, article No. 58, 25 pages
  3. Kumar, Schumacher and Shaw, 2013, Cloud microphysical effects of turbulent mixing and entrainment, Theor. Comput. Fluid Dyn. 27(3), 361-376
  4. Schumacher, Scheel, Krasnov, Donzis, Yakhot and Sreenivasan, 2014, Small-scale universality in fluid turbulence, PNAS 111, 10961-10965
  5. Scheel and Schumacher, 2016, Global and local statistics in turbulent convection at low Prandtl numbers, J. Fluid Mech. 802, 147-173
  6. Pandey, Scheel and Schumacher, 2018, Turbulent superstructures in Rayleigh-Benard convection, Nat. Commun. 9, article No. 2118, 11 pages
  7. Giannakis, Kolchinskaya, Krasnov and Schumacher, 2018, Koopman analysis of the long-term analysis in a turbulent convection cell, J. Fluid Mech. 847, 735-767
  8. Fonda, Pandey, Schumacher and Sreenivasan, 2019, Deep learning in turbulent convection networks, PNAS 116, 8867-8672
  9. Schumacher and Sreenivasan, 2020, Colloquium: Unusual dynamics of convection in the Sun, Rev. Mod. Phys. 92(4), article No. 041001, 25 pages
  10. Pandey and Schumacher, 2020, Reservoir computing model of two-dimensional turbulent convection, Phys. Rev. Fluids 5(11), 113506
  11. Scheel and Schumacher, 2017, Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows, Phys. Rev. Fluids 2, 123501
  12. Bailon-Cuba, Emran and Schumacher, 2010, Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection, J. Fluid Mech. 655, 152
  13. Bailon-Cuba and Schumacher, 2011, Low-dimensional model of turbulent Rayleigh-Bénard convection in a Cartesian cell with square domain, Phys. Fluids 23, 077101
  14. Emran and Schumacher, 2015, Large-scale mean patterns in turbulent convection, J. Fluid Mech. 776, 96
  15. Hamlington, Schumacher and Dahm, 2008, W. J. A., Local and nonlocal strain rate fields and vorticity alignment in turbulent flows, Phys. Rev. E 77, 026303
  16. Heyder and Schumacher, 2021, Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection, Phys. Rev. E 103, 053107
  17. Pandey, Schumacher and Sreenivasan, 2021, Non-Boussinesq low-Prandtl-number convection with a temperature-dependent thermal diffusivity, Astrophys. J. 907, 56
  18. Pandey, Schumacher and Sreenivasan, 2020, A perspective on machine learning in turbulent flows, J. Turb. 21, 567
  19. Scheel, Emran and Schumacher, 2013, Resolving the fine-scale structure in turbulent Rayleigh-Bénard convection, New J. Phys. 15, 113063
  20. Schneide, Pandey, Padberg-Gehle and Schumacher, 2018, Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters, Phys. Rev. Fluids 3, 113501
  21. Schumacher,Sreenivasan and Yakhot, 2007, Asymptotic exponents from low-Reynolds-number flows, New J. Phys. 9, 89
  22. Schumacher, Eckhardt and Doering, 2010, Extreme vorticity growth in Navier-Stokes turbulence, Phys. Lett. A 374, 861
  23. Schumacher,Götzfried and Scheel, 2015, Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids, Proc. Nat. Acad. Sci. USA 112, 9530 
  24. Schumacherand Scheel, 2016, Extreme dissipation event due to plume collision in a turbulent convection cell, Phys. Rev. E 94, 043104
  25. Schumacher, Pandey, Yakhot and Sreenivasan, 2018, The transition to turbulence scaling in Rayleigh-Bénard convection, Phys. Rev. E 98, 033120
  26. Shi, Emran and Schumacher, 2012, Boundary layer structure in turbulent Rayleigh-Bénard convection, J. Fluid Mech. 706, 5
  27. Valori and Schumacher, 2021, Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow, Europhys. Lett. 134, 34004
  28. Vieweg, Scheel and  Schumacher, 2021, Supergranule aggregation for constant heat flux-driven turbulent convection, Phys. Rev. Res. 3, 013231 open access   
  29. Iyer, Scheel, Schumacher and Sreenivasan, 2020, Classical 1/3 scaling of convection holds up to Ra = 1015, PNAS 117,7594
 

Publikationen

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Krasnov, Dmitry; Listratov, Yaroslav; Kolesnikov, Yuri; Belyaev, Ivan; Pyatnitskaya, Natalia; Sviridov, Evgeniy; Zikanov, Oleg;
Transformation of a submerged flat jet under strong transverse magnetic field. - In: epl : a letters journal exploring the frontiers of physics.. - Les Ulis : EDP Sciences, 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
Valori, Valentina; Schumacher, Jörg;
Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow. - In: epl : a letters journal exploring the frontiers of physics.. - Les Ulis : EDP Sciences, 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
Belyaev, Ivan A.; Pyatnitskaya, Natalia Yu.; Luchinkin, Nikita A.; Krasnov, Dmitry; Kolesnikov, Yuri; Listratov, Yaroslav I.; Mironov, I.S.; Zikanov, Oleg; Sviridov, Evgeniy V.;
Flat liquid metal jet affected by a transverse magnetic field. - In: Magnetohydrodynamics. - Salaspils : Inst. of Physics, Univ. of Latvia, Bd. 57 (2021), 2, S. 211-222

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.



https://doi.org/10.22364/mhd.57.2.6
Leng, Xue-Yuan; Krasnov, Dmitry; Li, Ben-Wen; Zhong, Jin-Qiang;
Flow structures and heat transport in Taylor-Couette systems with axial temperature gradient. - In: Journal of fluid mechanics. - Cambridge [u.a.] : Cambridge Univ. Press, ISSN 1469-7645, Bd. 920 (2021), S. A42-1-A42-21

https://doi.org/10.1017/jfm.2021.430
Heyder, Florian; Schumacher, Jörg;
Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection. - In: Physical review. - Woodbury, NY : Inst., ISSN 2470-0053, Bd. 103 (2021), 5, S. 053107-1-053107-14

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.



https://doi.org/10.1103/PhysRevE.103.053107
Xu, Wei; Wang, Yin; He, Xiaozhou; Wang, Xiaoping; Schumacher, Jörg; Huang, Shi-Di; Tong, Penger;
Mean velocity and temperature profiles in turbulent Rayleigh-Bénard convection at low Prandtl numbers. - In: Journal of fluid mechanics. - Cambridge [u.a.] : Cambridge Univ. Press, ISSN 1469-7645, Bd. 918 (2021), S. A1-1-A1-20

We report a direct numerical simulation (DNS) study of the mean velocity and temperature profiles in turbulent Rayleigh-Bénard convection (RBC) at low Prandtl numbers (Pr). The numerical study is conducted in a vertical thin disk with Pr varied in the range 0.17 ≤ Pr ≤ 4.4 and the Rayleigh number (Ra) varied in the range 5 × 10^8 ≤ Ra ≤ 1 × 10^10. By varying Pr from 4.4 to 0.17, we find a sharp change of flow patterns for the large-scale circulation (LSC) from a rigid-body rotation to a near-wall turbulent jet. We numerically examine the mean velocity equation in the bulk region and find that the mean horizontal velocity profile u(z) can be determined by a balance equation between the mean convection and turbulent diffusion with a constant turbulent viscosity t. This balance equation admits a self-similarity jet solution, which fits the DNS data well. In the boundary-layer region, we find that both the mean temperature profile T(z) and u(z) can be determined by a balance equation between the molecular diffusion and turbulent diffusion. Within the viscous boundary layer, both u(z) and T(z) can be solved analytically and the analytical results agree well with the DNS data. Our careful characterisation of the mean velocity and temperature profiles in low-Pr RBC provides a further understanding of the intricate interplay between the LSC, plume emission and boundary-layer dynamics, and pinpoints the physical mechanism for the emergence of a pronounced LSC in low-Pr RBC.



https://doi.org/10.1017/jfm.2021.255
Lyu, Ze; Boeck, Thomas; Karcher, Christian;
Electromagnetic interaction between a permanent magnet and a sphere moving in liquid metal. - In: Experiments in fluids : experimental methods and their applications to fluid flow ; research journal.. - Berlin : Springer, ISSN 1432-1114, Volume 62 (2021), issue 5, article 109, Seite 1-16

We present a series of model experiments where an electrically non-conductive solid sphere moves inside a vertical column of liquid alloy GaInSn. The experimental setup consists of the liquid metal container, the sphere driving system and the permanent magnet with the attached force sensor. The sphere moves at a controllable constant velocity U0 and follows a straight route, which in turn generates a liquid metal flow around the sphere. This flow interacts with the localized magnetic field of the permanent magnet, and thus a weak reaction force on the magnet is generated. The force sensor attached on the magnet has a resolution of the order 10^-6. Upon elimination of high frequency noise, reproducible time-dependent signals for the forces on the magnet are obtained in the experiments for several Reynolds numbers Re between 160 and 2000. The force component Fz on the magnet parallel to the direction of particle motion exhibits a typical two-peak structure with different peak heights, whereas the transverse force component Fx resembles an antisymmetric pulse. The results demonstrate that the force sensor can detect the presence of a moving particle in a quiescent conducting liquid. They also show that the structure of the Fx signal can be reproduced with less variation and is less sensitive to the Reynolds number than the Fz signal. Moreover, the structure and magnitude of time-dependent Lorentz force signals can be reasonably predicted by a numerical model.



https://doi.org/10.1007/s00348-021-03209-4
Tabaei Kazerooni, Hamid; Zinchenko, Georgy; Schumacher, Jörg; Cierpka, Christian;
Electrical voltage by electron spin-vorticity coupling in laminar ducts. - In: Physical review fluids. - College Park, MD : APS, ISSN 2469-990X, Bd. 6 (2021), 4, S. 043703-1-043703-14

We report a linear scaling law for an electrical voltage as a function of the pressure drop in capillary pipes and ducts. This voltage is generated by a process which is termed spin hydrodynamic generation (SHDG), a result of the collective electron spin-coupling to the vorticity field in the laminar flow in combination with an inverse spin-Hall effect. We study this phenomenon in laminar duct flows with different width-to-height aspect ratios ranging from 1 (square ducts) to infinite (two dimensional channels). First, we analytically solve the governing Valet-Fert spin diffusion equations for the SHDG by means of the method of small parameters together with proper boundary conditions for the set of inhomogeneous elliptic partial differential equations. Second, the proposed linear scaling law is validated through a series of experiments using capillary tubes with rectangular and square cross sections. The experimental results show very good agreement to the analytically found scaling law. A subsequent substitution of the bulk velocity of the laminar wall-bounded flows by the pressure drop reveals a universal scaling law for the electrical voltage that incorporates all pipe and duct geometries which we could study in our experiments. Finally, the efficiency of the system is estimated for circular pipes, rectangular and square ducts. This study shows that the efficiency of a spin hydrodynamic generator is the same for a circular pipe and a square duct with the same diameter and height, respectively. Hence, due to the ease of manufacturing and the possibility to scale the experiments up to parallel settings in a compact form, micro-channels with a square cross section seem to be the optimum for a spin hydrodynamic generator.



https://doi.org/10.1103/PhysRevFluids.6.043703
Vieweg, Philipp P.; Schneide, Christiane; Padberg-Gehle, Kathrin; Schumacher, Jörg;
Lagrangian heat transport in turbulent three-dimensional convection. - In: Physical review fluids. - College Park, MD : APS, ISSN 2469-990X, Bd. 6 (2021), 4, S. L041501-1-L041501-9

Spatial regions that do not mix effectively with their surroundings and, thus, contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CSs) which we investigate here in direct numerical simulations in convection cells with a square cross section of aspect ratio [Gamma]=16, Rayleigh number Ra=10^5, and Prandtl numbers Pr=0.1,0.7, and 7. The analysis is based on N=524288 Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the detected CSs contribute by a third less to the global turbulent heat transport for all investigated Prandtl numbers compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.



https://doi.org/10.1103/PhysRevFluids.6.L041501
Vieweg, Philipp P.; Scheel, Janet D.; Schumacher, Jörg;
Supergranule aggregation for constant heat flux-driven turbulent convection. - In: Physical review research. - College Park, MD : APS, ISSN 2643-1564, Bd. 3 (2021), 1, S. 013231-1-013231-14

Turbulent convection processes in nature are often found to be organized in a hierarchy of plume structures and flow patterns. The gradual aggregation of convection cells or granules to a supergranule which eventually fills the whole horizontal layer is reported and analyzed in spectral element direct numerical simulations of three-dimensional turbulent Rayleigh-Bénard convection at an aspect ratio of 60. The formation proceeds over a time span of more than 104 convective time units for the largest accessible Rayleigh number and occurs only when the turbulence is driven by a constant heat flux which is imposed at the bottom and top planes enclosing the convection layer. The resulting gradual inverse cascade process is observed for both temperature variance and turbulent kinetic energy. An additional analysis of the leading Lyapunov vector field for the full turbulent flow trajectory in its high-dimensional phase space demonstrates that turbulent flow modes at a certain scale continue to give rise locally to modes with a longer wavelength in the turbulent case. As a consequence, successively larger convection patterns grow until the horizontal extension of the layer is reached. This instability mechanism, which is known to exist near the onset of constant heat flux-driven convection, is shown here to persist into the fully developed turbulent flow regime, thus connecting weakly nonlinear pattern formation with the one in fully developed turbulence. We discuss possible implications of our study for observed, but not yet consistently numerically reproducible, solar supergranulation which could lead to improved simulation models of surface convection in the Sun.



https://doi.org/10.1103/PhysRevResearch.3.013231