In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this expository article, we review the construction in [8] of a "Fluid computer" in dimension 3 that combines techniques in symbolic dynamics with the connection between steady Euler flows and contact geometry unveiled by Etnyre and Ghrist. In addition, we argue that the metric that renders the vector field Beltrami cannot be critical in the Chern-Hamilton sense [9]. We also sketch the completely different construction for the Euclidean metric in $\mathbb R^3$ as given in [7]. These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems.

翻译：1991年，Moore [20] 提出了流体动力学是否具备计算能力的问题。类似地，2016年，Tao [25] 探讨了包括流体在内的机械系统能否模拟通用图灵机。在这篇综述性文章中，我们回顾了文献[8]中提出的三维“流体计算机”构造，该构造将符号动力学技术与Etnyre和Ghrist所揭示的稳态欧拉流与接触几何之间的联系相结合。此外，我们论证了使向量场成为Beltrami流的度量不可能是Chern-Hamilton意义下的临界度量[9]。我们还概述了文献[7]中针对$\mathbb R^3$上欧几里得度量的完全不同的构造方法。这些结果揭示了不可判定的流体粒子轨迹的存在性。文章最后列出了一系列待解决的问题。