垂直管内浮力驱动交换流的双稳性
Bistability of buoyancy-driven exchange flows in vertical tubes
摘要：
浮力驱动的交换流在各种自然和工程系统中很常见，从持续活跃的火山到海洋海峡的逆流。本文用封闭垂直管内交换流动的实验作为替代，阐明了这种流动的基本特征。由此产生的数据历史上已被分析和解释，通过核心环空流动的解决方案，最常见的流动配置在有限的粘度对比。这些模型在拟合实验数据方面取得了成功，但在解释自然系统中观察到的变异性方面效果较差。在本文中，我们对垂直管内浮力驱动交换流的经典问题建立了核-环解。该模型假定存在两个数学上有效的解决方案，即薄和厚芯的解决方案。然而，理论上存在两个解并不一定意味着该系统在可能发生流切换的意义上是可解的。使用直接的数值模拟，我们测试的假设，即在垂直管的核心-环形流是不稳定的，这意味着实现的流场是不唯一的流动的材料参数定义。我们的数值实验，充分预测实验数据，没有拟合参数，表明浮力驱动的交换流确实是固有的非线性系统。这一发现与以前的实验数据是一致的，但与以前的分析模型的基本假设，即解决方案是唯一的，可以通过最大化系统中的通量或极值化耗散来确定。这些结果有重要的影响，数据解释的分析模型，也可能有相关的分歧，了解火山脱气。
英文摘要：
Buoyancy-driven exchange flows are common to a variety of natural and engineering systems ranging from persistently active volcanoes to counterflows in oceanic straits. Experiments of exchange flows in closed vertical tubes have been used as surrogates to elucidate the basic features of such flows. The resulting data have historically been analyzed and interpreted through core-annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we formulate a core-annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes. The model posits the existence of two mathematically valid solutions, i.e. thin- and thick-core solutions. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Using direct numerical simulations, we test the hypothesis that core-annular flow in vertical tubes is bistable, which implies that the realized flow field is not uniquely defined by the material parameters of the flow. Our numerical experiments, which fully predict experimental data without fitting parameters, demonstrate that buoyancy-driven exchange flows are indeed inherently bistable systems. This finding is consistent with previous experimental data, but in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. These results have important implications for data interpretation by analytical models, and may also have relevant ramifications for understanding volcanic degassing.
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