Propagating thermal vortex-ring as a generalisation of Hill's vortex
Yano, Jun-Ichi ; Flierl, Glenn R.
An analytical solution of the thermal vortex ring in the similarity regime is derived in this study. An attempt is first made to find a steadily-propagating solution as an extension of the Hill's vortex by considering its modification by buoyancy. However, the derived solution is incomplete, because the internal and external solutions cannot match properly. The unsteadiness of the system due to the presence of buoyancy removes this inconsistency. Separating dependencies in time and space leads to a temporal tendency of the vortex-ring radius proportional to t1/2 with t the time, as expected from the similarity solution. Modifications to the spatial dependency are relatively minor compared to the original steadily-propagating solution. The analytical solution overall reproduces the basic characteristics of thermal vortex rings found in recent numerical simulations, especially a negative dynamic drag, albeit in a very qualitative manner.</p>
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