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 in many fundamental questions which 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 problem. This theme issue surveys the progress recently made on a number of outstanding problems in this area using approaches that transcend traditional discipline boundaries, by combining modern methods of modeling, computation, and mathematical analysis.

This is the first part of a two-part issue. The second part is available here.

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