We discuss spatio-temporal pattern formation in two separate thermal convective systems. In the first system, hydrothermal waves (HTW) are modeled numerically in an annular channel. A temperature difference is imposed across the channel, which induces a surface tension gradient on the free surface of the fluid, leading to a surface flow towards the cold side. The flow pattern is axially symmetric along the temperature gradient with an internal circulation for a small temperature difference. This axially symmetric flow (ASF) becomes unstable beyond a given temperature difference threshold, and subsequently, symmetry-breaking flow, i. e., rotational oscillating waves or HTW appear. For the second system, Rayleigh–Bénard convection (RBC) is experimentally studied in the non-turbulent regime. When a thin film of liquid is heated, the competing forces of viscosity and buoyancy give rise to convective instabilities. This convective instability creates a spatio-temporal non-uniform temperature distribution on the surface of the fluid film. The surface temperature statistics are studied in both these systems as “order” and “disorder” phase separates. Although the mechanisms that give rise to convective instabilities are different in both cases, we find an agreement on the macroscopic nature of the thermal distributions in these emergent structures.

中文翻译：

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热对流系统中的模式形成：时空热统计、紧急通量和局部平衡

我们讨论了两个独立的热对流系统中的时空模式形成。在第一个系统中，热液波 (HTW) 在环形通道中进行数值模拟。跨通道施加温差，这在流体的自由表面上引起表面张力梯度，导致表面流向冷侧。流型沿温度梯度轴对称，具有小温差的内部循环。这种轴对称流（ASF）在超过给定的温差阈值后变得不稳定，随后出现对称破坏流，即旋转振荡波或HTW。对于第二个系统，Rayleigh-Bénard 对流 (RBC) 在非湍流状态下进行了实验研究。当一层薄薄的液体被加热时，粘度和浮力的竞争导致对流不稳定性。这种对流不稳定性在流体膜表面产生时空非均匀温度分布。表面温度统计在这两个系统中都被研究为“有序”和“无序”相分离。尽管在这两种情况下导致对流不稳定性的机制不同，但我们发现这些涌现结构中热分布的宏观性质是一致的。