Convection near threshold for Prandtl numbers near 1.
Convection near threshold for Prandtl numbers near 1.
复制标题
普朗特数接近 1 的阈值附近的对流。
DOI：
10.1103/physreve.48.4399
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Guenter Ahlers
中科院分区：
文献类型：
--
作者：
Yuchou Hu;Yuchou Hu;R. Ecke;R. Ecke;Guenter Ahlers;Guenter Ahlers
采用阴影成像和热输运测量，研究了两种不同侧壁、半径高比\ensuremath{\Gamma} =41和43的圆柱形对流。工质在25.3 bar时为${\mathrm{CO}}_{2}$，普朗特数\ensuremath{\sigma} =0.93。其中一个单元（\ensuremath{\Gamma} =43）在\ensuremath{\epsilon} == \ensuremath{\Delta} T/ \ensuremath{\Delta}${\mathit{T}}_{\mathit{c}}$ -1=0.19 （\ensuremath{\Delta}${\mathit{T}}_{\mathit{c}}$为临界温差）范围内，轴对称对流卷在开始以上是稳定的。同心圆图案的中心脐的振幅增长为${\mathrm{\ensuremath{\epsilon}}}_{1}^{\mathrm{\ensuremath{\beta}}}$，其近发病比外围大得多，${\mathrm{\ensuremath{\beta}}}_{1}$ =0.27 \ifmmode\pm\else\textpm\fi{} 0.04。脐外振幅增长为${\mathrm{\ensuremath{\epsilon}}}_{2}^{\mathrm{\ensuremath{\beta}}}$, ${\mathrm{\ensuremath{\beta}}}_{2}$ =0.48 \ifmmode\pm\else\textpm\fi{} 0.04。当\ensuremath{\Gamma} =41时，轴对称对流滚流与被限制在侧壁附近的环形横滚流共存是开始时的首选模式，并且在\ensuremath{\epsilon} = 0.08时保持稳定。随着\ensuremath{\epsilon}的增加，同心圆对流模式的脐略微偏离中心，但从未超过50% of the cell depth. For \ensuremath{\epsilon}g0.10, the patterns were unstable and evolved over many horizontal thermal diffusion times to straight-roll patterns with defects and grain boundaries. The process involved the umbilicus moving toward the sidewall, accompanied by radially traveling waves emitted by the umbilicus. While the umbilicus emitted, the crossrolls adjacent to the sidewall traveled parallel to the wall, and rolls were created and destroyed at a source and sink, respectively, presumably owing to large-scale flows generated by the off-centered position of the umbilicus.
Rayleigh-B\'enard convection in two cylindrical geometries with different sidewalls and with radius-to-height ratios \ensuremath{\Gamma}=41 and 43 was studied with shadowgraph imaging and heat-transport measurements. The working fluid was ${\mathrm{CO}}_{2}$ at 25.3 bar with a Prandtl number \ensuremath{\sigma}=0.93. For one of the cells (\ensuremath{\Gamma}=43), axisymmetric convection rolls were stable above onset up to \ensuremath{\epsilon}==\ensuremath{\Delta}T/\ensuremath{\Delta}${\mathit{T}}_{\mathit{c}}$-1=0.19, where \ensuremath{\Delta}${\mathit{T}}_{\mathit{c}}$ is the critical temperature difference. The amplitude of the center of the concentric patterns, the umbilicus, much larger near onset than that of the outlying region, grew as ${\mathrm{\ensuremath{\epsilon}}}_{1}^{\mathrm{\ensuremath{\beta}}}$, with ${\mathrm{\ensuremath{\beta}}}_{1}$=0.27\ifmmode\pm\else\textpm\fi{}0.04. Outside the umbilicus, the amplitude grew as ${\mathrm{\ensuremath{\epsilon}}}_{2}^{\mathrm{\ensuremath{\beta}}}$, with ${\mathrm{\ensuremath{\beta}}}_{2}$=0.48\ifmmode\pm\else\textpm\fi{}0.04. For \ensuremath{\Gamma}=41, axisymmetric convection rolls, coexisting with an annular cross-roll state confined near the sidewall, were the preferred patterns above onset and remained stable up to an \ensuremath{\epsilon} of 0.08. The umbilicus of the concentric convection pattern shifted slightly off center as \ensuremath{\epsilon} was increased, but the shift never exceeded 50% of the cell depth. For \ensuremath{\epsilon}g0.10, the patterns were unstable and evolved over many horizontal thermal diffusion times to straight-roll patterns with defects and grain boundaries. The process involved the umbilicus moving toward the sidewall, accompanied by radially traveling waves emitted by the umbilicus. While the umbilicus emitted, the crossrolls adjacent to the sidewall traveled parallel to the wall, and rolls were created and destroyed at a source and sink, respectively, presumably owing to large-scale flows generated by the off-centered position of the umbilicus.