Rayleigh-Taylor instability of an inclined buoyant viscous cylinder
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Lister, John R.; Kerr, Ross; Russell, Nick J; Crosby, Andrew
Description
The Rayleigh-Taylor instability of an inclined buoyant cylinder of one very viscous fluid rising through another is examined through linear stability analysis, numerical simulation and experiment. The stability analysis represents linear eigenmodes of a given axial wavenumber as a Fourier series in the azimuthal direction, allowing the use of separable solutions to the Stokes equations in cylindrical polar coordinates. The most unstable wavenumber k is long-wave if both the inclination angle...[Show more]
dc.contributor.author | Lister, John R. | |
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dc.contributor.author | Kerr, Ross | |
dc.contributor.author | Russell, Nick J | |
dc.contributor.author | Crosby, Andrew | |
dc.date.accessioned | 2015-12-10T23:24:09Z | |
dc.identifier.issn | 0022-1120 | |
dc.identifier.uri | http://hdl.handle.net/1885/67107 | |
dc.description.abstract | The Rayleigh-Taylor instability of an inclined buoyant cylinder of one very viscous fluid rising through another is examined through linear stability analysis, numerical simulation and experiment. The stability analysis represents linear eigenmodes of a given axial wavenumber as a Fourier series in the azimuthal direction, allowing the use of separable solutions to the Stokes equations in cylindrical polar coordinates. The most unstable wavenumber k is long-wave if both the inclination angle and the viscosity ratio (internal/external) are small; for this case, k max{, ( ln1)1/2} and thus a small angle in experiments can have a significant effect for 1. As increases, the maximum growth rate decreases and the upward propagation rate of disturbances increases; all disturbances propagate without growth if the cylinder is sufficiently close to vertical, estimated as 70. Results from the linear stability analysis agree with numerical calculations for = 1 and experimental observations. A point-force numerical method is used to calculate the development of instability into a chain of individual plumes via a complex three-dimensional flow. Towed-source experiments show that nonlinear interactions between neighbouring plumes are important for 20 and that disturbances can propagate out of the system without significant growth forα≳ 40. | |
dc.publisher | Cambridge University Press | |
dc.source | Journal of Fluid Mechanics | |
dc.subject | Keywords: Axial wave numbers; Azimuthal direction; Buoyancy driven instability; Eigen modes; Experimental observation; Inclination angles; low-Reynolds-number flows; Nonlinear interactions; Numerical calculation; Numerical simulation; Polar coordinate; Propagation buoyancy-driven instability; low-Reynolds-number flows | |
dc.title | Rayleigh-Taylor instability of an inclined buoyant viscous cylinder | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 671 | |
dc.date.issued | 2011 | |
local.identifier.absfor | 040403 - Geophysical Fluid Dynamics | |
local.identifier.ariespublication | f2965xPUB1399 | |
local.type.status | Published Version | |
local.contributor.affiliation | Lister, John R., University of Cambridge | |
local.contributor.affiliation | Kerr, Ross, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Russell, Nick J, University of Cambridge | |
local.contributor.affiliation | Crosby, Andrew, University of Cambridge | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 313 | |
local.bibliographicCitation.lastpage | 338 | |
local.identifier.doi | 10.1017/S0022112010005689 | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
local.identifier.absseo | 970102 - Expanding Knowledge in the Physical Sciences | |
local.identifier.absseo | 970104 - Expanding Knowledge in the Earth Sciences | |
dc.date.updated | 2016-02-24T08:13:33Z | |
local.identifier.scopusID | 2-s2.0-79952816123 | |
local.identifier.thomsonID | 000288100100013 | |
Collections | ANU Research Publications |
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