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

Kalogirou, Anna and Blyth, Mark G. (2023) Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel. Journal of Fluid Mechanics, 955. ISSN 0022-1120

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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.

Item Type: Article
Additional Information: Supplementary movie: available at
Uncontrolled Keywords: channel flow,lubrication theory,condensed matter physics,mechanics of materials,mechanical engineering,applied mathematics ,/dk/atira/pure/subjectarea/asjc/3100/3104
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 27 Jan 2023 18:30
Last Modified: 27 Feb 2023 10:31
DOI: 10.1017/jfm.2022.1070


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