SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 1, Page 510-540, January 2020.
This work applies a continuous data assimilation scheme---a framework for reconciling sparse and potentially noisy observations to a mathematical model---to Rayleigh--Bénard convection at infinite or large Prandtl numbers using only the temperature field as observables. These Prandtl numbers are applicable to the earth's mantle and to gases under high pressure. We rigorously identify conditions that guarantee synchronization between the observed system and the model, then confirm the applicability of these results via numerical simulations. Our numerical experiments show that the analytically derived conditions for synchronization are far from sharp; that is, synchronization often occurs even when sufficient conditions of our theorems are not met. We also develop estimates on the convergence of an infinite Prandtl model to a large (but finite) Prandtl number generated set of observations. Numerical simulations in this hybrid setting indicate that the mathematically rigorous results are accurate, but of practical interest only for extremely large Prandtl numbers.

中文翻译：

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热测量中大PrandtlRayleigh-Bénard对流中的数据同化

SIAM应用动力系统杂志，第19卷，第1期，第510-540页，2020年1月。
这项工作将连续数据同化方案（一种用于将稀疏和可能有噪声的观测值与数学模型进行调和的框架）应用于仅使用温度场作为可观测值的无限或大Prandtl值的Rayleigh-Bénard对流。这些普朗特数适用于地球的地幔和高压气体。我们严格地确定条件，以保证观察的系统和模型之间的同步，然后通过数值模拟确认这些结果的适用性。我们的数值实验表明，分析得出的同步条件远非那么尖锐。也就是说，即使不满足我们定理的充分条件，也经常会发生同步。我们还针对将无限Prandtl模型收敛到大量（但有限）Prandtl数生成的观测值进行收敛的估计。在这种混合设置下的数值模拟表明，严格的数学结果是准确的，但仅对极大的Prandtl数有意义。