Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry. (10th October 2020)

• Record Type: Journal Article
• Authors: Zhao, Zhiye; Wang, Pei; Liu, Nansheng; Lu, Xiyun
• Is Part Of: Journal of fluid mechanics. Volume 900(2020)
• Publication Date: 2020-10-10
• Subjects: buoyancy-driven instability, -- nonlinear instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.526
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : We present an analytical model of nonlinear evolution of two-dimensional single-mode Rayleigh–Taylor instability (RTI) in cylindrical geometry at arbitrary Atwood number for the first time. Our model covers a full scenario of bubble evolution from the earlier exponential growth to the nonlinear regime with the bubbles growing in time as $\frac {1}{2}a_{b}t^2$ for cylindrical RTI, other than as $V_{b}t$ for planar RTI, where $a_{b}$ and $V_{b}$ are the bubble acceleration and velocity, respectively. It is found that from this model the saturating acceleration $a_{b}$ is formulated as a simplified function of the external acceleration, Atwood number and number of perturbation waves. This model's predictions are in good agreement with data from direct numerical simulations.