Temporal dynamics of large-scale structures for turbulent Rayleigh–Bénard convection in a moderate aspect-ratio cylinder

Sakievich, P. J.; Peet, Y. T.; Adrian, R. J.

doi:10.1017/jfm.2020.588

Temporal dynamics of large-scale structures for turbulent Rayleigh–Bénard convection in a moderate aspect-ratio cylinder

Journal Article · Wed Sep 02 00:00:00 EDT 2020 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2020.588· OSTI ID:1670180

^[1]; Peet, Y. T. ^[2]; ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Arizona State Univ., Tempe, AZ (United States)

We investigate the spatial organization and temporal dynamics of large-scale, coherent structures in turbulent Rayleigh–Bénard convection via direct numerical simulation of a 6.3 aspect-ratio cylinder with Rayleigh and Prandtl numbers of 9.6×10⁷ and 6.7, respectively. Fourier modal decomposition is performed to investigate the structural organization of the coherent turbulent motions by analysing the length scales, time scales and the underlying dynamical processes that are ultimately responsible for the large-scale structure formation and evolution. We observe a high level of rotational symmetry in the large-scale structure in this study and that the structure is well described by the first four azimuthal Fourier modes. Two different large-scale organizations are observed during the duration of the simulation and these patterns are dominated spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. Studies of the transition between these two large-scale patterns, radial and vertical variations in the azimuthal energy spectra, as well as the spatial and modal variations in the system's correlation time are conducted. Rotational dynamics are observed for individual Fourier modes and the global structure with strong similarities to the dynamics that have been reported for unit aspect-ratio domains in prior works. It is shown that the large-scale structures have very long correlation time scales, on the order of hundreds to thousands of free-fall time units, and that they are the primary source for a horizontal inhomogeneity within the system that can be observed during a finite, but a very long-time simulation or experiment.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: Arizona State University's Dean's Fellowship; National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1670180

Alternate ID(s):: OSTI ID: 1670726

Report Number(s):: SAND--2019-13881J; SAND--2020-5368J; 686278

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 901; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

References (51)

An Overlapping Schwarz Method for Spectral Element Solution of the Incompressible Navier–Stokes Equations Fischer, Paul F. Journal of Computational Physics, Vol. 133, Issue 1 https://doi.org/10.1006/jcph.1997.5651	journal	May 1997
Spectral Methods in Fluid Dynamics Canuto, Claudio; Hussaini, M. Yousuff; Quarteroni, Alfio Springer Berlin, Heidelberg https://doi.org/10.1007/978-3-642-84108-8	book	January 1988
Turbulent thermal convection in wide horizontal fluid layers Adrian, R. J.; Ferreira, R. T. D. S.; Boberg, T. Experiments in Fluids, Vol. 4, Issue 3 https://doi.org/10.1007/BF00280263	journal	May 1986
Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection Grötzbach, Günther Journal of Computational Physics, Vol. 49, Issue 2 https://doi.org/10.1016/0021-9991(83)90125-0	journal	February 1983
High-order splitting methods for the incompressible Navier-Stokes equations Karniadakis, George Em; Israeli, Moshe; Orszag, Steven A. Journal of Computational Physics, Vol. 97, Issue 2 https://doi.org/10.1016/0021-9991(91)90007-8	journal	December 1991
Patterns of convective turbulence: an effect of Prandtl number Malevsky, Andrei V. Physics of the Earth and Planetary Interiors, Vol. 88, Issue 1 https://doi.org/10.1016/0031-9201(94)05074-8	journal	February 1995
Coherent structures in turbulent convection, an experimental study Zocchi, Giovanni; Moses, Elisha; Libchaber, Albert Physica A: Statistical Mechanics and its Applications, Vol. 166, Issue 3 https://doi.org/10.1016/0378-4371(90)90064-Y	journal	July 1990
Scaling of velocity and temperature fluctuations in turbulent thermal convection Fernandes, R. L. J.; Adrian, R. J. Experimental Thermal and Fluid Science, Vol. 26, Issue 2-4 https://doi.org/10.1016/S0894-1777(02)00147-4	journal	June 2002
Large-scale thermal motions of turbulent Rayleigh–Bénard convection in a wide aspect-ratio cylindrical domain Sakievich, P. J.; Peet, Y. T.; Adrian, R. J. International Journal of Heat and Fluid Flow, Vol. 61 https://doi.org/10.1016/j.ijheatfluidflow.2016.04.011	journal	October 2016
Large-scale patterns in Rayleigh–Bénard convection von Hardenberg, J.; Parodi, A.; Passoni, G. Physics Letters A, Vol. 372, Issue 13 https://doi.org/10.1016/j.physleta.2007.10.099	journal	March 2008
High-Order Methods for Incompressible Fluid Flow Deville, M. O.; Fischer, P. F.; Mund, E. H. Cambridge University Press https://doi.org/10.1017/CBO9780511546792	book	January 2009
Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection Brown, Eric; Ahlers, Guenter Journal of Fluid Mechanics, Vol. 568 https://doi.org/10.1017/S0022112006002540	journal	November 2006
Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection Funfschilling, Denis; Brown, Eric; Ahlers, Guenter Journal of Fluid Mechanics, Vol. 607 https://doi.org/10.1017/S0022112008001882	journal	June 2008
Oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection: the sloshing mode and its relationship with the torsional mode Zhou, Quan; Xi, Heng-Dong; Zhou, Sheng-Qi Journal of Fluid Mechanics, Vol. 630 https://doi.org/10.1017/S0022112009006764	journal	July 2009
The origin of oscillations of the large-scale circulation of turbulent Rayleigh–Bénard convection Brown, Eric; Ahlers, Guenter Journal of Fluid Mechanics, Vol. 638 https://doi.org/10.1017/S0022112009991224	journal	October 2009
Experimental investigation of the structure of large- and very-large-scale motions in turbulent pipe flow Bailey, Sean C. C.; Smits, Alexander J. Journal of Fluid Mechanics, Vol. 651 https://doi.org/10.1017/S0022112009993983	journal	March 2010
Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection Bailon-Cuba, J.; Emran, M. S.; Schumacher, J. Journal of Fluid Mechanics, Vol. 655 https://doi.org/10.1017/S0022112010000820	journal	May 2010
Dynamics of reorientations and reversals of large-scale flow in Rayleigh–Bénard convection Mishra, P. K.; De, A. K.; Verma, M. K. Journal of Fluid Mechanics, Vol. 668 https://doi.org/10.1017/S0022112010004830	journal	December 2010
Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number Cioni, S.; Ciliberto, S.; Sommeria, J. Journal of Fluid Mechanics, Vol. 335 https://doi.org/10.1017/S0022112096004491	journal	March 1997
Prandtl number effects in convective turbulence Verzicco, R.; Camussi, R. Journal of Fluid Mechanics, Vol. 383 https://doi.org/10.1017/S0022112098003619	journal	March 1999
Scaling in thermal convection: a unifying theory Grossmann, Siegfried; Lohse, Detlef Journal of Fluid Mechanics, Vol. 407 https://doi.org/10.1017/S0022112099007545	journal	March 2000
Structural organization of large and very large scales in turbulent pipe flow simulation Baltzer, J. R.; Adrian, R. J.; Wu, Xiaohua Journal of Fluid Mechanics, Vol. 720 https://doi.org/10.1017/jfm.2012.642	journal	February 2013
Large-scale mean patterns in turbulent convection Emran, Mohammad S.; Schumacher, Jörg Journal of Fluid Mechanics, Vol. 776 https://doi.org/10.1017/jfm.2015.316	journal	July 2015
Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow Krug, Dominik; Lohse, Detlef; Stevens, Richard J. A. M. Journal of Fluid Mechanics, Vol. 887 https://doi.org/10.1017/jfm.2019.1054	journal	January 2020
Combined measurement of velocity and temperature in liquid metal convection Zürner, Till; Schindler, Felix; Vogt, Tobias Journal of Fluid Mechanics, Vol. 876 https://doi.org/10.1017/jfm.2019.556	journal	August 2019
Turbulent superstructures in Rayleigh-Bénard convection Pandey, Ambrish; Scheel, Janet D.; Schumacher, Jörg Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-04478-0	journal	May 2018
Fluctuations in turbulent Rayleigh–Bénard convection: The role of plumes Grossmann, Siegfried; Lohse, Detlef Physics of Fluids, Vol. 16, Issue 12 https://doi.org/10.1063/1.1807751	journal	December 2004
Oscillations of the large scale wind in turbulent thermal convection Resagk, Christian; du Puits, Ronald; Thess, André Physics of Fluids, Vol. 18, Issue 9 https://doi.org/10.1063/1.2353400	journal	September 2006
A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh–Bénard convection Brown, Eric; Ahlers, Guenter Physics of Fluids, Vol. 20, Issue 7 https://doi.org/10.1063/1.2919806	journal	July 2008
Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection Brown, Eric; Ahlers, Guenter Physics of Fluids, Vol. 20, Issue 10 https://doi.org/10.1063/1.2991432	journal	October 2008
Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows Munters, Wim; Meneveau, Charles; Meyers, Johan Physics of Fluids, Vol. 28, Issue 2 https://doi.org/10.1063/1.4941912	journal	February 2016
Jump rope vortex in liquid metal convection Vogt, Tobias; Horn, Susanne; Grannan, Alexander M. Proceedings of the National Academy of Sciences, Vol. 115, Issue 50 https://doi.org/10.1073/pnas.1812260115	journal	November 2018
Large-scale flow generation in turbulent convection Krishnamurti, R.; Howard, L. N. Proceedings of the National Academy of Sciences, Vol. 78, Issue 4 https://doi.org/10.1073/pnas.78.4.1981	journal	April 1981
Resolving the fine-scale structure in turbulent Rayleigh–Bénard convection Scheel, Janet D.; Emran, Mohammad S.; Schumacher, Jörg New Journal of Physics, Vol. 15, Issue 11 https://doi.org/10.1088/1367-2630/15/11/113063	journal	November 2013
Mean wind and its reversal in thermal convection Sreenivasan, K. R.; Bershadskii, A.; Niemela, J. J. Physical Review E, Vol. 65, Issue 5 https://doi.org/10.1103/PhysRevE.65.056306	journal	May 2002
Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection Grossmann, Siegfried; Lohse, Detlef Physical Review E, Vol. 66, Issue 1 https://doi.org/10.1103/PhysRevE.66.016305	journal	July 2002
Effect of inertia in Rayleigh-Bénard convection Breuer, M.; Wessling, S.; Schmalzl, J. Physical Review E, Vol. 69, Issue 2 https://doi.org/10.1103/PhysRevE.69.026302	journal	February 2004
Azimuthal motion of the mean wind in turbulent thermal convection Xi, Heng-Dong; Zhou, Quan; Xia, Ke-Qing Physical Review E, Vol. 73, Issue 5 https://doi.org/10.1103/PhysRevE.73.056312	journal	May 2006
Breakdown of wind in turbulent thermal convection du Puits, Ronald; Resagk, Christian; Thess, André Physical Review E, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevE.75.016302	journal	January 2007
Ability of a low-dimensional model to predict geometry-dependent dynamics of large-scale coherent structures in turbulence Bai, Kunlun; Ji, Dandan; Brown, Eric Physical Review E, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevE.93.023117	journal	February 2016
Turbulent thermal superstructures in Rayleigh-Bénard convection Stevens, Richard J. A. M.; Blass, Alexander; Zhu, Xiaojue Physical Review Fluids, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevFluids.3.041501	journal	April 2018
Origin of the Temperature Oscillation in Turbulent Thermal Convection Xi, Heng-Dong; Zhou, Sheng-Qi; Zhou, Quan Physical Review Letters, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevLett.102.044503	journal	January 2009
Initial stages of pattern formation in Rayleigh-Bénard convection Meyer, Christopher W.; Ahlers, Guenter; Cannell, David S. Physical Review Letters, Vol. 59, Issue 14 https://doi.org/10.1103/PhysRevLett.59.1577	journal	October 1987
Thermal Convection for Large Prandtl Numbers Grossmann, Siegfried; Lohse, Detlef Physical Review Letters, Vol. 86, Issue 15 https://doi.org/10.1103/PhysRevLett.86.3316	journal	April 2001
Large Scale Structures in Rayleigh-Bénard Convection at High Rayleigh Numbers Hartlep, T.; Tilgner, A.; Busse, F. H. Physical Review Letters, Vol. 91, Issue 6 https://doi.org/10.1103/PhysRevLett.91.064501	journal	August 2003
Plume Motion and Large-Scale Circulation in a Cylindrical Rayleigh-Bénard Cell Funfschilling, Denis; Ahlers, Guenter Physical Review Letters, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevLett.92.194502	journal	May 2004
Reorientation of the Large-Scale Circulation in Turbulent Rayleigh-Bénard Convection Brown, Eric; Nikolaenko, Alexei; Ahlers, Guenter Physical Review Letters, Vol. 95, Issue 8 https://doi.org/10.1103/PhysRevLett.95.084503	journal	August 2005
Large-Scale Circulation Model for Turbulent Rayleigh-Bénard Convection Brown, Eric; Ahlers, Guenter Physical Review Letters, Vol. 98, Issue 13 https://doi.org/10.1103/PhysRevLett.98.134501	journal	March 2007
XSEDE: Accelerating Scientific Discovery Towns, John; Cockerill, Timothy; Dahan, Maytal Computing in Science & Engineering, Vol. 16, Issue 5 https://doi.org/10.1109/MCSE.2014.80	journal	September 2014
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Recent Developments in Rayleigh-Bénard Convection Bodenschatz, Eberhard; Pesch, Werner; Ahlers, Guenter Annual Review of Fluid Mechanics, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.fluid.32.1.709	journal	January 2000