Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada.
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada.
Philos Trans A Math Phys Eng Sci. 2022 Jun 27;380(2226):20210057. doi: 10.1098/rsta.2021.0057. Epub 2022 May 9.
Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problems. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
流体动力学是物理学和应用数学的交叉领域，其应用范围在自然科学和工程领域不断扩大。然而，尽管经过几十年的协同研究，这个领域仍然存在许多尚未解决的基本问题。这些问题的核心往往是数学模型，通常以偏微分方程的形式存在，而许多悬而未决的问题都涉及到这些模型的有效性，以及可以从这些模型中学到什么关于物理问题。近年来，在这一领域的许多开放性问题上都取得了重大进展，这些进展通常采用超越传统学科界限的方法，通过结合现代建模、计算和数学分析方法来实现。本期特刊的两部分主题旨在代表这些方法的广泛性，重点关注本质上是数学问题但有助于理解实际物理重要方面的问题，如流体动力稳定性、输运、混合、耗散和涡动力学。本文是特刊“物理流体动力学中的数学问题（第二部分）”的一部分。
