2019/10/10 by Vasconcelos, Giovani L., Cordeiro, Luan P., Brum, Arthur A. +1
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.1910.04327
Inviscid bubble dynamics in a viscous fluid, moving with velocity V far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. The well-posed (after a Tikhonov regularization) dynamical system provides an extensive list of unsteady closed form solutions due to integrability. A new (rational) class of solutions is obtained and added to the logarithmic class found earlier (Phys. Rev. E 89, 061003(R), 2014). The only attractor selects the observable bubble shape and velocity U = 2V from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results illustrate the most salient aspects of the bubble dynamics.