Abstract
The recent work of Rooney & Linden (1996) is generalized
to describe the motion
of non-Boussinesq plumes in both uniform and stratified environments. Using
an
integral model in which the horizontal entrainment velocity is assumed
to take the
form uε=α(ρ¯/ρe)
1/2w
where α is the entrainment coefficient, ρ¯ is the plume
density,
w the plume velocity and ρe the
ambient density, it is shown that the vertical scale
over which non-Boussinesq effects are significant is given by
zB=5/3
(B2o/
(20α4g3))1/5
where Bo is the buoyancy flux at the source.
In a
uniform environment, the system admits similarity solutions such that the
location of the source of a real plume lies a distance
zB[mid ]ρo/Δρ[mid ]
−5/3 beyond the point source of the similarity solution.
The above entrainment law implies a fundamental difference between the
motion
of upward and downward propagating non-Boussinesq plumes, with the radius
of
upward propagating plumes being greater than that of the equivalent Boussinesq
plume, while the radius of downward propagating plumes is smaller. In a
stratified
but incompressible environment the model predicts that non-Boussinesq effects
are
confined close to the source and that at each height, the plume velocity
and
the fluxes
of mass, momentum and buoyancy coincide exactly with those of the equivalent
Boussinesq plume. Furthermore, at the neutral buoyancy height, the plume
radius
equals that of the equivalent Boussinesq plume.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
47 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献