Dynamics of bubbles in supernovae and turbulent vortices

We consider the motion of a bubble in a central acceleration field created by gravity or a centrifugal force. In the former case, the bubble moves outwards from and, in the latter, towards the center. We have calculated the characteristic time needed for a bubble to leave or reach the center. The solution obtained provides insight into the processes of thermonuclear supernovae and combustion; in other words, into the interaction between a flame and a turbulent vortex. In the case of combustion, a light bubble of burnt material propagates towards the axis of a strong turbulent vortex faster than it drifts in the direction of rotation of the vortex. It is expected that the development of bubbles should prevent the formation of “pockets” at the flame front, similar to those predicted by a simplified model of turbulent combustion in a constant density flux. In the case of a thermonuclear supernova in a deflagration burning regime, it is shown that light products of burning rise from the center of the white dwarf substantially more rapidly than the thermonuclear flame front propagates. As a result, a flame cannot completely burn the central part of the star, and instead is pushed to the outer layers of the white dwarf. The effect of bubble motion (large-scale convection) makes spherically symmetric models for thermonuclear supernovae unrealistic, which is of prime importance for the supernova spectrum and energy. The motion of bubbles is even faster in the case of a rotating white dwarf; under certain conditions, the centrifugal force may dominate over the gravitational force. To test this theory, we have carried out numerical simulations of supernovae explosions for various sizes of the burned region in the core of the presupernova. We have derived a relation between the rate of large-scale convection and the size of the burned region, which is specified by the rate of the deflagration in the thermonuclear burning.