Dynamics of viscous vortex knots and links

Abstract: Reconnection is the process by which two approaching vortices cut and connect to each other. As a topologically changing event, it has been a subject of considerable fundamental interest for decades – not only in (classical) viscous flows but also in quantum fluids, as well as in numerous other fields, such as plasmas, polymers, DNAs, and so on. For viscous fluid flows, reconnection is believed to play a significant role in various important phenomena, such as turbulence cascade, fine-scale mixing, and aerodynamic noise generation. We first delineate the underlying mechanism involved in vortex reconnection and its apparent role in turbulence cascade. Then we address the helicity dynamics involved in viscous reconnection occurring in evolutions of a trefoil knotted vortex and a Hopf-link. For both cases, we find that the global helicity H gradually decreases before reconnection but sharply increases during reconnection – this effect increases with increasing vortex Reynolds number (Re≡circulation/viscousity). This suggests that H for viscous flows is not conserved as Re→∞. Both positive and negative helical structures are simultaneously generated before and during reconnection, and their different decay rates due to asymmetric reconnection appears to cause such an increase of H during reconnection. By examining the topological aspects of the helicity dynamics, we find that different from H, the sum of linking and writhing numbers (i.e., Lk+Wr) continuously drop during reconnection. Our results suggest that the twist, which increases with Re, plays a more important role in helicity dynamics than recognized before, particularly at high Re.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology