Applications of Arnold's variational principle to the stability of vortices in ideal and viscous flows
Duration: 1 hour 9 mins
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Thierry Gallay (Université Grenoble Alpes)
16 February 2022 – 09:45 to 10:45 |
|---|
| Created: | 2022-02-23 15:18 |
|---|---|
| Collection: | Mathematical aspects of turbulence: where do we stand? |
| Publisher: | Isaac Newton Institute |
| Copyright: | Thierry Gallay |
| Language: | eng (English) |
| Abstract: | We revisit Arnold's variational approach to the stability of steady-state solutions of the two-dimensional Euler equations. In the
case of planar vortices, we study in detail the quadratic form that represents the second variation of the energy on the isovortical surface. We show in particular that, for a large class of radially symmetric vortices with strictly decreasing profile, the second variation is negative definite for all perturbations that preserve the total circulation. We use that property to give a new stability proof for the Oseen vortex as a self-similar solution of the 2D Navier-Stokes equations, and to investigate the vanishing viscosity limit of axisymmetric vortex rings. This talk is based on joint work with V. Sverak. |
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| MPEG-4 Video | 1280x720 | 2.15 Mbits/sec | 1.09 GB | View | Download | |
| MPEG-4 Video | 640x360 | 682.26 kbits/sec | 344.80 MB | View | Download | |
| WebM | 1280x720 | 1.26 Mbits/sec | 656.02 MB | View | Download | |
| WebM | 768x360 | 217.19 kbits/sec | 63.66 MB | View | Download | |
| iPod Video | 480x270 | 489.1 kbits/sec | 247.18 MB | View | Download | |
| MP3 | 44100 Hz | 253.21 kbits/sec | 127.97 MB | Listen | Download | |
| Auto * | (Allows browser to choose a format it supports) | |||||