We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time $t_{heat}$ . The experiments are performed over the flux Rayleigh number ( $Ra_f$ ) range $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ and the Prandtl number ( $Pr$ ) range $28.6 \leq Pr \leq 904.7$ . The corresponding Rayleigh number ( $Ra= t_{heat}\,Ra_{f}/\tau _0\,Pr$ ) range is $900 \leq Ra \leq 4\times 10^{4}$ , where $\tau _0$ is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as $t_{emit}$ , $t_{recover}$ and $t_{static}$ , correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their $Ra_f$ – $Pr$ dependencies are found to be $t_{emit}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$ , $t_{recover}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ and $t_{static}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$ , respectively. Thermal structures generated by finite $t_{heat}$ exhibit similar evolution dynamics once $t_{heat} \ge t_{emit}$ , with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the $Ra$ -dependence from $Ra$ to $(Ra\ln Ra)^{0.5}$ at $Ra \simeq 6000$ ; and their maximum acceleration reaches the value of starting plumes at $t_{heat}\simeq t_{recover}$ , and remains unchanged for larger $t_{heat}$ . In particular, the maximum rising velocity for the cases with $t_{heat} = t_{recover}$ follows a scaling relation $Ra_f^{0.37}\,Pr^{-0.37}$ , in contrast to the relation $Ra_f^{0.48}\,Pr^{-0.48}$ for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection.

中文翻译：

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层流热结构的形成和演化：与热边界层的相关性和加热时间的影响

我们报告了由小热源产生的层流热结构的形成和演化的实验研究，重点是它们与热边界层的相关性和加热时间的影响 $t_{热量}$ 。实验是在通量瑞利数 ( $Ra_f$ ） 范围 $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ 和普朗特数（ $Pr$ ） 范围 $28.6 \leq Pr \leq 904.7$ 。对应的瑞利数（ $Ra= t_{热量}\,Ra_{f}/\tau _0\,Pr$ ）范围是 $900 \leq Ra \leq 4\times 10^{4}$ ， 在哪里 $\tau_0$ 是扩散时间尺度。对于连续加热（即起始羽流）产生的热结构，其形成过程存在三个特征时间，这三个特征时间很好地反映了热边界层厚度的变化。这些特征时间，表示为 $t_{发出}$ , $t_{恢复}$ 和 $t_{静态}$ ，分别对应于羽流发射开始和完成的时刻，以及热边界层变为准静态的时刻。他们的 $Ra_f$ – $Pr$ 发现依赖关系是 $t_{发射}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$ , $t_{恢复}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ 和 $t_{静态}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$ ， 分别。由有限生成的热结构 $t_{热量}$ 表现出类似的进化动态一次 $t_{热量} \ge t_{发射}$ ，加速阶段的行为类似于起始羽流，而衰变阶段的行为类似于热气流（即有限量的浮力流体）。进一步发现它们的最大上升速度经历了一个转变 $Ra$ - 依赖于 $Ra$ 到 $(Ra\ln Ra)^{0.5}$ 在 $Ra \simeq 6000$ ;并且它们的最大加速度达到起始羽流的值 $t_{热量}\simeq t_{恢复}$ ，并且对于更大的情况保持不变 $t_{热量}$ 。特别是，对于以下情况，最大上升速度 $t_{热量} = t_{恢复}$ 遵循比例关系 $Ra_f^{0.37}\,Pr^{-0.37}$ ，与关系相反 $Ra_f^{0.48}\,Pr^{-0.48}$ 用于启动羽流。这项研究提供了对层流热结构的更全面的了解，层流热结构与自然和实验室系统中的一系列过程相关，例如瑞利-贝纳德对流。