Abstract
Consider the dynamics of a toroidal bubble, taking into account the displacement of its circular axis~ Let the toroidal gas bubble, with radius of the circular axis a and radius of the cross section R0, be initially in the horizontal plane in an unbounded incompressible fluid of density 0The fluid pressure inside the bubble is p0, the fluid pressure at the depth of location of the bubble is p~, and the bubble has a vertical velocity V. The dynamics of the bubble includes two basic components: the pulsating motion near the circular axis due to the pressure difference P0 -p~ and the motion in the vertical direction due to the presence of vertical velocity and the buoyancy force.
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