Vortex formation in ellipsoidal thermal bubbles

Abstract

The rise of an isolated dry thermal bubble in a quiescent unstratified environment is a prototypical natural convective flow. This study considers the rise of an isolated dry thermal bubble of ellipsoidal shape (elliptical in both horizontal and vertical cross sections). The azimuthat asymmetry of the bubble allows the vorticity tilting mechanism to operate without an environmental wind. The dry Boussinesq equations of motion are solved analytically as a Taylor series in time for the early time behavior of the bubble (involving derivatives of up to the third order in time). The analytic results are supplemented with numerical simulations to examine the longer-time behavior. The first nonzero term in the Taylor expansion for the vertical vorticity is a third-order term, and appears as a four-leaf clover pattern with lobes of alternating sign. The horizontal flow associated with this vorticity pattern first appears as a sheared stagnation point-type flow, but eventually organizes into vertical vortices that fill the bubble. The vortices induce large structural changes to the bubble and eventually reverse the sense of the azimuthal asymmetry.