Symmetry breaking and vortex formation in two-dimensional turbulence, a talk by Erik Lindborg (KTH Royal Institute of Technology)
Abstract
Fjørtoft (1953) showed that there are two types of interactions in triads of wave number modes in a two-dimensional non-divergent flow. The first type is where the middle mode acts as a source for each of the two other modes and the second type is where it acts as a sink. Kraichnan (1967) showed that the first type is dominant in a self-similar upscale energy cascade as well as in a downscale enstrophy cascade. In this presentation, I will formulate an independent argument suggesting first type interactions are generally efficient in transferring energy upscale and enstrophy downscale, while second type interactions are equally efficient in transferring energy and enstrophy in the opposite directions. An energy source introduces symmetry breaking in favour of first type interactions and triads in the vicinity of the source are caught in chains of interactions of this type, explaining why energy is transferred upscale and enstrophy downscale of the source. I will argue that there are situations when subsets of triads can be caught in chains of interactions of the second type, leading to downscale energy and upscale enstrophy transfer. I also hypothesize that vortex formation is a physical space manifestation of such chains. The observed slowing down of the upscale energy cascade observed in many simulations may thus be related to increased activation of second type interactions as the cascade moves upscale.
This talk will be given remotely, via MS Teams. Please contact Gemma Reeves to register for attendance at this Scottish branch talk. Please note that email addresses will be sent on to the hosts at St Andrews who are running the event video conferencing. Email addresses will be used solely for purposes of adding guests to the seminar meeting on MS Teams and communicating a link to join the seminar meeting.
No charge is made to attend meetings. Non-IMA members are welcome.
