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Axisymmetric plumes in viscous fluids

Citation

Allwright, EJ and Forbes, LK and Walters, SJ, Axisymmetric plumes in viscous fluids, ANZIAM Journal, 61, (2) pp. 119-147. ISSN 1446-1811 (2019) [Refereed Article]

Copyright Statement

Copyright 2019 Australian Mathematical Society

DOI: doi:10.1017/S1446181119000075

Abstract

We consider fluid in a channel of finite height. There is a circular hole in the channel bottom, through which fluid of a lower density is injected and rises to form a plume. Viscous boundary layers close to the top and bottom of the channel are assumed to be so thin that the viscous fluid effectively slips along each of these boundaries. The problem is solved using a novel spectral method, in which Hankel transforms are first used to create a steady-state axisymmetric (inviscid) background flow that exactly satisfies the boundary conditions. A viscous correction is then added, so as to satisfy the time-dependent Boussinesq Navier–Stokes equations within the fluid, leaving the boundary conditions intact. Results are presented for the "lazy" plume, in which the fluid rises due only to its own buoyancy, and we study in detail its evolution with time to form an overturning structure. Some results for momentum-driven plumes are also presented, and the effect of the upper wall of the channel on the evolution of the axisymmetric plume is discussed.

Item Details

Item Type:Refereed Article
Keywords:Boussinesq fluid, overturning plume, unsteady flow
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Allwright, EJ (Ms Emma Allwright)
UTAS Author:Forbes, LK (Professor Larry Forbes)
UTAS Author:Walters, SJ (Mr Stephen Walters)
ID Code:137087
Year Published:2019
Funding Support:Australian Research Council (DP140100094)
Deposited By:Mathematics
Deposited On:2020-01-30
Last Modified:2020-05-20
Downloads:0

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