2019/01/30 by Changsheng Dou, Jialiang Wang, Dou, Changsheng +3
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1901.11012
correct the authors' information in arXiv:1811.11610. arXiv admin note: substantial text overlap with arXiv:1811.11610 by other authors
openalex publication_date 2019/01/30 · openalex created_date 2019/02/21 · arxiv created 2021/02/20 · arxiv updated 2021/05/06 · openalex updated_date 2026/07/28
We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold ϑ\rm c) by modified variational method of PDEs. Moreover we find a new upper bound for Λ. In particular, we observe from the upper bound that Λ decreasingly converges to zero, as ϑ goes from zero to the threshold ϑ\rm c. The convergence behavior of Λ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.