Bodenschatz, Eberhard

[["dc.bibliographiccitation.firstpage","436"],["dc.bibliographiccitation.journal","Journal of Fluid Mechanics"],["dc.bibliographiccitation.lastpage","467"],["dc.bibliographiccitation.volume","758"],["dc.contributor.author","Ahlers, Guenter"],["dc.contributor.author","Bodenschatz, Eberhard"],["dc.contributor.author","He, Xiaozhou"],["dc.date.accessioned","2018-11-07T09:33:15Z"],["dc.date.available","2018-11-07T09:33:15Z"],["dc.date.issued","2014"],["dc.description.abstract","We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical sample with an aspect ratio (diameter D over height L) equal to 0.50, in both the classical and the ultimate state. The measurements are for Rayleigh numbers Ra from 6 x 10(11) to 10(13) in the classical and 7 x 10(14) to 1.1 x 10(15) (our maximum accessible Ra) in the ultimate state. The Prandtl number was close to 0.8. Although to lowest order the bulk is often assumed to be isothermal in the time average, we found a 'logarithmic layer' (as reported briefly by Ahlers et al., Phys. Rev. Lett., vol. 109, 2012, 114501) in which the reduced temperature Theta = [< T-(z) - T-m]/Delta T (with T-m the mean temperature, Delta T the applied temperature difference and <...> a time average) varies as A ln (z/L) + B or A' ln (1 - z/L + B' with the distance z from the bottom plate of the sample. In the classical state, the amplitudes -A and A' are equal within our resolution, while in the ultimate state there is a small difference, with -A/A' similar or equal to 0.95. For the classical state, the width of the log layer is approximately 0.1L, the same near the top and the bottom plate as expected for a system with reflection symmetry about its horizontal midplane. For the ultimate state, the log-layer width is larger, extending through most of the sample, and slightly asymmetric about the midplane. Both amplitudes A and A' vary with radial position r, and this variation can be described well by A = A(0) [(R - r)/R](-0.65), where R is the radius of the sample. In the classical state, these results are in good agreement with direct numerical simulations (DNS) for Ra = 2 x 10(12); in the ultimate state there are as yet no DNS. The amplitudes -A and A' varied as Ra-eta, with eta similar or equal to 0.12 in the classical and eta similar or equal to 0.18 in the ultimate state. A close analogy between the temperature field in the classical state and the 'law of the wall' for the time-averaged downstream velocity in shear flow is discussed. A two-sublayer mean-field model of the temperature profile in the classical state was analysed and yielded a logarithmic z dependence of Theta. The Ra dependence of the amplitude A given by the model corresponds to an exponent eta(th) D 0.106, in good agreement with the experiment. In the ultimate state the experimental result eta similar or equal to 0.18 differs from the prediction eta(th) similar or equal to 0.043 by Grossmann & Lohse (Phys. Fluids, vol. 24, 2012, 125103)."],["dc.identifier.doi","10.1017/jfm.2014.543"],["dc.identifier.fs","606693"],["dc.identifier.isi","000343757900020"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/12950"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/31927"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Cambridge Univ Press"],["dc.relation.issn","1469-7645"],["dc.relation.issn","0022-1120"],["dc.relation.orgunit","Fakultät für Physik"],["dc.title","Logarithmic temperature profiles of turbulent Rayleigh-Benard convection in the classical and ultimate state for a Prandtl number of 0.8"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","103012"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","New Journal of Physics"],["dc.bibliographiccitation.volume","14"],["dc.contributor.affiliation","Ahlers, Guenter;"],["dc.contributor.affiliation","He, Xiaozhou;"],["dc.contributor.affiliation","Funfschilling, Denis;"],["dc.contributor.affiliation","Bodenschatz, Eberhard;"],["dc.contributor.author","Ahlers, Guenter"],["dc.contributor.author","He, Xiaozhou"],["dc.contributor.author","Funfschilling, Denis"],["dc.contributor.author","Bodenschatz, Eberhard"],["dc.date.accessioned","2018-11-07T09:04:46Z"],["dc.date.available","2018-11-07T09:04:46Z"],["dc.date.issued","2012"],["dc.date.updated","2022-02-10T04:36:21Z"],["dc.description.abstract","We report on the experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Benard convection (RBC) in a cylindrical sample of aspect ratio Gamma equivalent to D/L = 0.50 (D = 1.12m is the diameter and L = 2.24m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bar as the fluid. They are for the Rayleigh-number range 3 x 10(12) less than or similar to Ra less than or similar to 10(15) and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra-1 similar or equal to 1.4 x 10(13) we find Nu = N-0 Ra-gamma eff with gamma(eff) = 0.312 +/- 0.002, which is consistent with classical turbulent RBC in a system with laminar boundary layers below the top and above the bottom plate. For Ra-1 < Ra < Ra-2 (with Ra-2 similar or equal to 5 x 10(14)) gamma(eff) gradually increases up to 0.37 +/- 0.01. We argue that above Ra-2 the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for Gamma = 0.50 are re-examined and compared with our results. Some of them show a transition to a state with gamma(eff) in the range from 0.37 to 0.40, albeit at values of Ra in the range from 9 x 10(10) to 7 x 10(11) which is much lower than the present Ra-1 or Ra-2 . The nature of the transition found by them is relatively sharp and does not reveal the wide transition range observed in this work. In addition to the results for the genuine Rayleigh-Benard system, we present measurements for a sample which was not completely sealed; the small openings permitted external currents, imposed by density differences and gravity, to pass through the sample. That system should no longer be regarded as genuine RBC because the externally imposed currents modified the heat transport in a major way. It showed a sudden decrease of gamma(eff) from 0.308 for Ra < Ra-t similar or equal to 4 x 10(13) to 0.25 for larger Ra. A number of possible experimental effects are examined in a sequence of appendices; none of these effects is found to have a significant influence on the measurements."],["dc.identifier.doi","10.1088/1367-2630/14/10/103012"],["dc.identifier.eissn","1367-2630"],["dc.identifier.fs","599453"],["dc.identifier.isi","000309396700004"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/9984"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/25176"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","IOP Publishing"],["dc.relation.issn","1367-2630"],["dc.relation.orgunit","Fakultät für Physik"],["dc.rights","CC BY-NC-SA 3.0"],["dc.rights.uri","https://creativecommons.org/licenses/by-nc-sa/3.0/"],["dc.title","Heat transport by turbulent Rayleigh–Bénard convection for Pr ≃ 0.8 and 3 × 1012 ≲ Ra ≲ 1015: aspect ratio Γ = 0.50"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","123001"],["dc.bibliographiccitation.issue","12"],["dc.bibliographiccitation.journal","New Journal of Physics"],["dc.bibliographiccitation.volume","11"],["dc.contributor.affiliation","Ahlers, Guenter;"],["dc.contributor.affiliation","Funfschilling, Denis;"],["dc.contributor.affiliation","Bodenschatz, Eberhard;"],["dc.contributor.author","Ahlers, Guenter"],["dc.contributor.author","Funfschilling, Denis"],["dc.contributor.author","Bodenschatz, Eberhard"],["dc.date.accessioned","2018-11-07T11:21:43Z"],["dc.date.available","2018-11-07T11:21:43Z"],["dc.date.issued","2009"],["dc.date.updated","2022-02-09T16:00:27Z"],["dc.description.abstract","We describe a pressure vessel for conducting experiments in helium (He), air, nitrogen (N-2) or sulfur hexafluoride (SF6) under pressures of up to 19 bars, and facilities for the study of Rayleigh-Benard convection inside this pressure vessel. The convection cells, known as the high pressure convection facilities (HPCFs), can have interior heights up to L = 2.3 m and diameters up to D = 1.2 m. Measurements of the Nusselt number Nu for Rayleigh numbers Ra up to Ra = 4 x 10(13) and a Prandtl number Pr similar or equal to 0.8 gave Nu proportional to Ra-gamma eff with gamma(eff) similar or equal to 0.308. At Ra there was a sharp transition to a new regime. The Nusselt number was continuous at Ra , but the exponent characterizing its dependence on Ra changed suddenly to gamma(eff) = 0.25. Near Ra = Ra similar or equal to 3 x 10(14), there was a further change in the Ra-dependence of Nu. A new state with gamma(eff) similar or equal to 0.17 evolved and there was bistability of the gamma(eff) = 0.25 and the gamma(eff) = 0.17 branches."],["dc.identifier.doi","10.1088/1367-2630/11/12/123001"],["dc.identifier.eissn","1367-2630"],["dc.identifier.isi","000272471000001"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?goescholar/4053"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55843"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1367-2630"],["dc.relation.orgunit","Fakultät für Physik"],["dc.rights","Goescholar"],["dc.rights.access","openAccess"],["dc.rights.uri","https://goedoc.uni-goettingen.de/licenses"],["dc.subject.ddc","530"],["dc.title","Transitions in heat transport by turbulent convection at Rayleigh numbers up to 10(15)"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","063028"],["dc.bibliographiccitation.journal","New Journal of Physics"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","He, Xiaozhou"],["dc.contributor.author","van Gils, Dennis P. M."],["dc.contributor.author","Bodenschatz, Eberhard"],["dc.contributor.author","Ahlers, Guenter"],["dc.date.accessioned","2018-11-07T09:55:44Z"],["dc.date.available","2018-11-07T09:55:44Z"],["dc.date.issued","2015"],["dc.description.abstract","We report results of Reynolds-number measurements, based on multi-point temperature measurements and the elliptic approximation (EA) of He and Zhang (2006 Phys. Rev. E 73 055303), Zhao and He (2009 Phys. Rev. E 79 046316) for turbulent Rayleigh-Benard convection (RBC) over the Rayleigh-number range 10(11) less than or similar to Ra less than or similar to 2 x 10(14) and for a Prandtl number Pr similar or equal to 0.8. The sample was a right-circular cylinder with the diameter D and the height L both equal to 112 cm. The Reynolds numbers Re-U and Re-V were obtained from the mean-flow velocity U and the root-mean-square fluctuation velocity V, respectively. Both were measured approximately at the mid-height of the sample and near (but not too near) the side wall close to a maximum of Re-U. A detailed examination, based on several experimental tests, of the applicability of the EA to turbulent RBC in our parameter range is provided. The main contribution to Re-U came from a large-scale circulation in the form of a single convection roll with the preferred azimuthal orientation of its down flow nearly coinciding with the location of the measurement probes. First we measured time sequences of Re-U(t) and Re-V(t) from short (10 s) segments which moved along much longer sequences of many hours. The corresponding probability distributions of Re-U(t) and Re-V(t) had single peaks and thus did not reveal significant flow reversals. The two averaged Reynolds numbers determined from the entire data sequences were of comparable size. For Ra < Ra-1 similar or equal to 2 x 10(13) both Re-U and Re-V could be described by a power-law dependence on Ra with an exponent zeta close to 0.44. This exponent is consistent with several other measurements for the classical RBC state at smaller Ra and larger Pr and with the Grossmann-Lohse (GL) prediction for Re-U (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse 2001 86 3316; Grossmann and Lohse 2002 66 016305) but disagrees with the prediction zeta similar or equal to 0.33 by GL (Grossmann and Lohse 2004 Phys. Fluids 16 4462) for Re-V. At Ra = Ra-2 similar or equal to 7 x 10(13) the dependence of Re-V on Ra changed, and for larger Ra Re-V similar to Ra-0.50 +/- 0.02, consistent with the prediction for Re-U (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse Phys. Rev. Lett. 2001 86 3316; Grossmann and Lohse Phys. Rev. E 2002 66 016305; Grossmann and Lohse 2012 Phys. Fluids 24 125103) in the ultimate state of RBC."],["dc.identifier.doi","10.1088/1367-2630/17/6/063028"],["dc.identifier.isi","000358929400003"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/13646"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/36813"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1367-2630"],["dc.relation.orgunit","Fakultät für Physik"],["dc.rights","CC BY 3.0"],["dc.title","Reynolds numbers and the elliptic approximation near the ultimate state of turbulent Rayleigh-Benard convection"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]