Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’ compiled and edited by Charles R. Doering, David Goluskin, Bartosz Protas and Jean-Luc Thiffeault

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

This issue is available to buy in print. Visit our information for readers page for purchasing options.

INTRODUCTION

Introduction
Editorial: Mathematical problems in physical fluid dynamics: part II
Published:09 May 2022Article ID:20210057

https://doi.org/10.1098/rsta.2021.0057

ARTICLES

Research articles
Remarks on stationary and uniformly rotating vortex sheets: flexibility results
Published:09 May 2022Article ID:20210045

https://doi.org/10.1098/rsta.2021.0045

Research articles
On the dynamics of point vortices for the two-dimensional Euler equation with Lp vorticity
Published:09 May 2022Article ID:20210046

https://doi.org/10.1098/rsta.2021.0046

Research articles
Equations of motion for weakly compressible point vortices
Published:09 May 2022Article ID:20210052

https://doi.org/10.1098/rsta.2021.0052

Research articles
Self-similarity in turbulence and its applications
Published:09 May 2022Article ID:20210048

https://doi.org/10.1098/rsta.2021.0048

Research articles
On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models
Published:09 May 2022Article ID:20210050

https://doi.org/10.1098/rsta.2021.0050

Research articles
Continuing invariant solutions towards the turbulent flow
Published:09 May 2022Article ID:20210031

https://doi.org/10.1098/rsta.2021.0031

Research articles
Self-similar hierarchy of coherent tubular vortices in turbulence
Published:09 May 2022Article ID:20210053

https://doi.org/10.1098/rsta.2021.0053

Research articles
Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment
Published:09 May 2022Article ID:20210033

https://doi.org/10.1098/rsta.2021.0033

Research articles
On the Prandtl–Kolmogorov 1-equation model of turbulence
Published:09 May 2022Article ID:20210054

https://doi.org/10.1098/rsta.2021.0054

Research articles
Geometric microcanonical theory of two-dimensional truncated Euler flows
Published:09 May 2022Article ID:20210049

https://doi.org/10.1098/rsta.2021.0049

Research articles
Spontaneous symmetry breaking for extreme vorticity and strain in the three-dimensional Navier–Stokes equations
Published:09 May 2022Article ID:20210051

https://doi.org/10.1098/rsta.2021.0051

Research articles
Extreme events in transitional turbulence
Published:09 May 2022Article ID:20210036

https://doi.org/10.1098/rsta.2021.0036

Research articles
Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment
Published:09 May 2022Article ID:20210030

https://doi.org/10.1098/rsta.2021.0030

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