Abstract
We generate vortex tangles using a Hopf flow on a 3-sphere, in place of the standard torus defined by periodic boundary conditions. These tangles are highly anisotropic, with vortices tending to align along the flow direction. Standard power law dependences change accordingly from their values in more isotropic tangles. The line length density $\langle L\rangle$ is proportional to $v_{ns}^{1.28}$, where $v_{ns}$ is the drive velocity, and the reconnection rate depends roughly on $\langle L\rangle^2$. We also discuss the effect of the full Biot-Savart law versus the local induction approximation (LIA). Under LIA the tangle collapses so that all vortices are nearly aligned with a single flow line, in sharp contrast to the torus where they become perpendicular to the driving velocity. Finally we present a few torus simulations with a helical velocity field, which in some ways resembles the 3-sphere flow.
Highlights
The notoriously intractable equations governing fluid flow generate a great deal of numerical work [1,2,3,4]
We find that the statistical behavior of tangles is independent of the initial conditions for the calculations, as shown in Fig. 5 for initial setups that differ by more than a factor of five in vortex line length
As with our previous simulations with the usual periodic boundary conditions [11], we examine the effects of including nonlocal terms only for vortices within a distance dNL
Summary
The notoriously intractable equations governing fluid flow generate a great deal of numerical work [1,2,3,4]. An example encountered in vortex filament simulations is the tendency of vortices to fall into an “open-orbit” state, where they align parallel to each other and perpendicular to the driving velocity field [7,8] In this configuration they interact only trivially with the velocity field, resulting in uniform translation of the entire set of vortices, so the open-orbit state persists indefinitely. The particular case of the open-orbit state can be prevented by including nonlocal interaction terms between vortices in addition to the Arms-Hama local term [9], but it demonstrates the possibility of topological artifacts This raises the question of how else the topology may affect simulation results.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
