Thermal vortex ring: vortex-dynamics analysis of a high-resolution simulation

• Published in: Journal of fluid mechanics 2024-08, Vol.991
• Main Authors: Yano, Jun-Ichi, Morrison, Hugh
• Format: Article
• Language: English
• Subjects: Balances (scales); Budgets; Components; Dimensional analysis; High resolution; JFM Papers; Physics; Potential vorticity; Power spectrum analysis; Propagation; Redundancy; Reynolds number; Simulation; Spin dynamics; Thermal simulation; Two dimensional analysis; Two dimensional flow; Vortex rings; Vortices; Vorticity
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2024.485

A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by $s^n$ with $n=-1$, 0, 1, where $s$ is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with $n=-1$). Analysis of the budget supports this description.