Turbulent entrainment into natural gravity-driven flows

Observations of entrainment into natural gravity-driven flows on sloping surfaces are described. It is shown that the laboratory-based entrainment law of Ellison & Turner (1959), which is often used for modelling of atmospheric and oceanic flows, underestimates the entrainment rates substantiall...

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Bibliographic Details
Published in:Journal of fluid mechanics 2005-06, Vol.533, p.259-268
Main Authors: PRINCEVAC, M., FERNANDO, H. J. S., WHITEMAN, C. D.
Format: Article
Language:English
Subjects:
ATMOSPHERIC CIRCULATION
COMPUTERIZED SIMULATION
Convection, turbulence, diffusion. Boundary layer structure and dynamics
Earth, ocean, space
ENTRAINMENT
ENVIRONMENTAL SCIENCES
EQUATIONS
Exact sciences and technology
External geophysics
layer
Meteorology
plumes
REYNOLDS NUMBER
RICHARDSON NUMBER
Schmidt
Water flow
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Description
Summary:Observations of entrainment into natural gravity-driven flows on sloping surfaces are described. It is shown that the laboratory-based entrainment law of Ellison & Turner (1959), which is often used for modelling of atmospheric and oceanic flows, underestimates the entrainment rates substantially, arguably due to the fact that the laboratory flows have been conducted at Reynolds numbers $(Re \lesssim 10^3)$ below what is required for mixing transition ($Re\sim10^3$–10^4) whereas natural flows occur at much higher Reynolds numbers $(Re\sim10^7)$. A new entrainment law of the form $E\sim Ri^{-3/4}$ is proposed for the atmospheric Richardson number range $0.15 \lt Ri \lt 1.5$. In contrast to the laboratory observation that entrainment ceases at $Ri = 0.8$, field observations show continuous entrainment over the entire Richardson number range.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112005004441