# Topological fluid dynamics for fluid dynamicists

@inproceedings{Childress2004TopologicalFD, title={Topological fluid dynamics for fluid dynamicists}, author={Stephen Childress}, year={2004} }

These notes are preliminary and informal. My aim is to provide an introduction to some of the basic ideas that have emerged in recent decades in the fluids literature that have a fundamentally topological character. That is, rather than focusing on details such as velocity profile or pressure field, this material deals with persistent invariant properties of a flow field, features which often have a geometric interpretation. A basic reference is the book of Arnold and Khesin [1]. Other…

## 7 Citations

### Manifolds in Fluid Dynamics

- Mathematics
- 2011

In studying fluid dynamics it is useful to employ two different perspectives of a fluid flowing through a domain D. The Eulerian point of view is to consider a fixed point x ∈ D, and observe the…

### Potentially singular solutions of the 3D axisymmetric Euler equations

- PhysicsProceedings of the National Academy of Sciences
- 2014

This paper attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by describing a class of rotationally symmetric flows from which infinitely fast spinning vortices can form in finite time.

### Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation

- MathematicsMultiscale Model. Simul.
- 2014

A local analysis near the point of the singularity suggests the existence of a self-similar blowup in the meridian plane and a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries.

### POTENTIALLY SINGULAR SOLUTIONS OF THE 3D INCOMPRESSIBLE EULER EQUATIONS

- Mathematics
- 2018

Whether the 3D incompressible Euler equations can develop a singularity in ﬁnite time from smooth initial data is one of the most challenging problems in mathematical ﬂuid dynamics. This work…

### On Woltjer's force‐free minimizers and Moffatt's magnetic relaxation

- MathematicsBulletin of the London Mathematical Society
- 2022

In this note, we exhibit a situation where a stationary state of Moffatt's ideal magnetic relaxation problem is different than the corresponding force‐free L2$L^2$ energy minimizer of Woltjer's…

### Adding Semi-Structured Automated Grid Generation and the Menter-Shear Stress Turbulence Transport Model for Internal Combustion Engine Simulations to Novel FEM LANL Combustion Codes

- Engineering
- 2019

The addition of GridPro semi-structured, automated generation of grids for complex moving boundaries for combustion engine applications and the Menter Shear Stress Turbulent Transfer (SST) model are…

### Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study

- MathematicsSIAM Rev.
- 2019

Whether the three-dimensional incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics...

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