Turbulent Lagrangian dynamics of vortex and magnetic-field line

Duration: 33 mins 57 secs

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/22780/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Turbulent Lagrangian dynamics of vortex and magnetic-field line's image

Description:	Eyink, GL (Johns Hopkins) Thursday 02 October 2008, 10:30-11:00

Created:

2008-10-23 10:23

Collection:

The Nature of High Reynolds Number Turbulence

Publisher:

Isaac Newton Institute

Eyink, GL

Language:

eng (English)

Credits:

Author:

Eyink, GL


Abstract:	We do not understand the laws of motion of vortex and magnetic-field lines in high-Reynolds-number turbulent flows. The current lore is self-contradictory. On the one hand, vortex/magnetic-field lines are often assumed to wander and elongate nearly as material lines in the limit of small viscosity/resistivity, and thus also to intensify, as a consequence of the Kelvin/Alfvén theorems. On the other hand, the topology of the lines is assumed to be continuously altered by viscous/resistive reconnection, implying breakdown of those same theorems. We discuss experimental and numerical evidence that these laws are both sometimes observed and sometimes violated in high-Reynolds-number turbulence. Unfortunately, we have no rational criterion to say when the Kelvin/Alfvén theorems or the Helmholtz laws of ``frozen-in'' motion should hold and when they should not. The problem has grown more perplexing with the theoretical discovery of "spontaneous stochasticity" for Lagrangian particle evolution in a Kolmogorov inertial range. As a consequence of the forgetting of initial separations in Richardson pair-diffusion, Lagrangian trajectories are not unique and must be replaced with random distributions of trajectories in the limit of small viscosity. This result presents a major crisis to our understanding of the turbulent dynamics of vortex/magnetic-field lines. As a possible resolution, we discuss a conjectured generalization of the Kelvin/Alfvén theorems, namely, that they survive as "backward martingales" of the spontaneous stochastic flows at high Reynolds-number. This conjectured relation provides a precise mathematical framework for the theory of turbulent reconnection. We discuss current rigorous results related to the conjecture and also important questions for investigation by experiment and simulation. A seminar from the Inertial-Range Dynamics and Mixing conference in association with the Newton Institute programme: The Nature of High Reynolds Number Turbulence www.newton.ac.uk/programmes/HRT/seminars/

Abstract:

We do not understand the laws of motion of vortex and magnetic-field lines in high-Reynolds-number turbulent flows. The current lore is self-contradictory. On the one hand, vortex/magnetic-field lines are often assumed to wander and elongate nearly as material lines in the limit of small viscosity/resistivity, and thus also to intensify, as a consequence of the Kelvin/Alfvén theorems. On the other hand, the topology of the lines is assumed to be continuously altered by viscous/resistive reconnection, implying breakdown of those same theorems. We discuss experimental and numerical evidence that these laws are both sometimes observed and sometimes violated in high-Reynolds-number turbulence. Unfortunately, we have no rational criterion to say when the Kelvin/Alfvén theorems or the Helmholtz laws of ``frozen-in'' motion should hold and when they should not. The problem has grown more perplexing with the theoretical discovery of "spontaneous stochasticity" for Lagrangian particle evolution in a Kolmogorov inertial range. As a consequence of the forgetting of initial separations in Richardson pair-diffusion, Lagrangian trajectories are not unique and must be replaced with random distributions of trajectories in the limit of small viscosity. This result presents a major crisis to our understanding of the turbulent dynamics of vortex/magnetic-field lines. As a possible resolution, we discuss a conjectured generalization of the Kelvin/Alfvén theorems, namely, that they survive as "backward martingales" of the spontaneous stochastic flows at high Reynolds-number. This conjectured relation provides a precise mathematical framework for the theory of turbulent reconnection. We discuss current rigorous results related to the conjecture and also important questions for investigation by experiment and simulation.

A seminar from the Inertial-Range Dynamics and Mixing conference in association with the Newton Institute programme: The Nature of High Reynolds Number Turbulence www.newton.ac.uk/programmes/HRT/seminars/

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	480x360	1.83 Mbits/sec	467.87 MB	View	Download
WebM	450x360	769.54 kbits/sec	190.51 MB	View	Download
Flash Video	480x360	804.24 kbits/sec	200.57 MB	View	Download
iPod Video	480x360	503.24 kbits/sec	125.51 MB	View	Download
QuickTime	384x288	844.64 kbits/sec	210.64 MB	View	Download
MP3	44100 Hz	125.04 kbits/sec	30.82 MB	Listen	Download
Windows Media Video		475.4 kbits/sec	118.56 MB	View	Download
Auto *	(Allows browser to choose a format it supports)