Dynamics of a viscous layer flowing radially over an inviscid ocean

We present a theoretical and experimental study of a viscous fluid layer spreading over a deep layer of denser, inviscid fluid. Specifically, we study an axisymmetric flow produced by a vertical line source. Close to the source, the flow is controlled viscously, with a balance between radial compres...

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Bibliographic Details
Published in:Journal of fluid mechanics 2012-04, Vol.696, p.152-174
Main Authors: Pegler, Samuel S., Worster, M. Grae
Format: Article
Language:English
Subjects:
Asymptotic properties
Compressive properties
Computational fluid dynamics
Earth, ocean, space
Exact sciences and technology
External geophysics
Fluid dynamics
Fluid flow
Fluid mechanics
Gravity
Hoop stress
Ice shelves
Mathematical analysis
Physics of the oceans
Sea ice
Spreading
Stresses
Thermohaline structure and circulation. Turbulence and diffusion
Thin films
Viscosity
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Summary:We present a theoretical and experimental study of a viscous fluid layer spreading over a deep layer of denser, inviscid fluid. Specifically, we study an axisymmetric flow produced by a vertical line source. Close to the source, the flow is controlled viscously, with a balance between radial compressive stresses and hoop stresses. Further out, the flow is driven by gradients in the buoyancy force and is resisted by viscous extensional and hoop stresses. An understanding of these different fluid-mechanical relationships is developed by asymptotic analyses for early times and for the near and far fields at late times. Confirmation of the late-time, far-field behaviour is obtained from a series of laboratory experiments in which golden syrup was injected into denser solutions of potassium carbonate. We use our mathematical solutions to discuss a physical mechanism by which horizontal viscous stresses in a spreading ice shelf, such as those in West Antarctica, can buttress the grounded ice sheet that supplies it.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2012.21