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Title: A viscous buoyancy-driven flow exhibiting finite-time blow-up
Authors: Kay, Anthony
Keywords: Blow-up
Buoyancy-driven flow
Viscous flow
Issue Date: 2013
Publisher: Oxford University Press on behalf of the Institute of Mathematics and its Applications / © The Author
Citation: KAY, A., 2013. A viscous buoyancy-driven flow exhibiting finite-time blow-up. IMA Journal of Applied Mathematics, 78 (6), pp. 1214 - 1236.
Abstract: We consider 2D viscous flow driven by buoyancy forces resulting from a quadratic horizontal density variation in an unbounded domain between horizontal walls. The density is a quadratic function of the concentration of a tracer, so we solve the vorticity equation under the Boussinesq approximation, together with an advection–diffusion equation for the tracer. Stagnation-point similitude eliminates dependence on the horizontal coordinate. For the case of small Grashof number (large viscosity), the flow passes through three stages. A transient adjusts from the initial condition of static fluid to a regime in which buoyancy and viscous forces are in balance. The flow and temperature gradient slowly intensify until eventually the non-linear advection terms become dominant. The flow then enters its final stage, in which a more rapid intensification leads to a singularity in finite time. While no rigorous proof has been found that this blow-up occurs, the combination of asymptotic analysis and numerical computation provides strong support for its occurrence.
Description: This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record KAY, A., 2013. A viscous buoyancy-driven flow exhibiting finite-time blow-up. IMA Journal of Applied Mathematics, 78 (6), pp. 1214 - 1236 is available online at: http://dx.doi.org/10.1093/imamat/hxs018
Version: Accepted for publication
DOI: 10.1093/imamat/hxs018
URI: https://dspace.lboro.ac.uk/2134/16476
Publisher Link: http://dx.doi.org/10.1093/imamat/hxs018
ISSN: 0272-4960
Appears in Collections:Published Articles (Maths)

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