Effect of viscosity on two-dimensional single-mode Rayleigh-Taylor instability during and after the reacceleration stage

In this paper, two-dimensional (2D) single-mode Rayleigh-Taylor instability with a low Atwood number (A = 0.15) at different Reynolds (Re) numbers (100 ≤ Re ≤ 10 000) is simulated, and the evolution of the bubble velocity and the bubble vorticity at different viscosities (or equivalently Re) after the quasisteady stage is investigated in detail. Special attention is paid for flows with a medium Reynolds number (200 ≤ Re ≤ 1000), and two new findings are summarized as follows: (1) At the reacceleration stage, we found that the vorticity near the bubble head is linearly inhibited by the viscosity. Based on this discovery, the dimensionless relationship between the vorticity intensity, viscosity, and time is formulated. (2) After the reacceleration stage, we found a new deceleration-acceleration stage, in which the bubble velocity is decelerated and accelerated repeatedly. This stage occurs because the vorticity near the bubble head is first decreased due to the inhibition of viscosity and then increased again when a pair of new Kelvin-Helmholtz instability-induced vortices approaches the bubble head. Consequently, the bubble velocity decelerates and accelerates correspondingly.