Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

Kalogirou, A.; Blyth, M.G.

Abstract

The Rayleigh-Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau-Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.

Citation

Kalogirou, A., & Blyth, M. (2023). Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel. Journal of Fluid Mechanics, 955, Article A32. https://doi.org/10.1017/jfm.2022.1070

• Journal Article Type: Article
• Acceptance Date: Dec 11, 2022
• Online Publication Date: Jan 18, 2023
• Publication Date: Jan 25, 2023
• Deposit Date: Dec 14, 2022
• Publicly Available Date: Jul 19, 2023
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 955
• Article Number: A32
• DOI: https://doi.org/10.1017/jfm.2022.1070
• Public URL: https://nottingham-repository.worktribe.com/output/14888745
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/nonlinear-dynamics-of-unstably-stratified-twolayer-shear-flow-in-a-horizontal-channel/7F288257CAEBDE66568048609C3D47DB
• Additional Information: Copyright: © The Author(s), 2023. Published by Cambridge University Press; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.; Free to read: This content has been made available to all.