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Axisymmetric plumes in viscous fluids

journal contribution
posted on 2023-05-20, 10:19 authored by Allwright, EJ, Lawrence ForbesLawrence Forbes, Stephen WaltersStephen Walters
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.


Australian Research Council


Publication title

ANZIAM Journal








School of Natural Sciences


Australian Mathematics Publ Assoc Inc

Place of publication

Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200

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Copyright 2019 Australian Mathematical Society

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