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Unformatted text preview: ty theory (1916).
The unstable fluid will tend to form convection cells about as
wide as they are deep (unit aspect ratio).
Rayleighs theory is a search for the least perturbation that will
cause overturning of the unstable fluid. This mode is called
the least stable or most unstable mode.
The Rayleigh number of a fluid yields the relative ease with
which a temperature perturbation, ∆ T, will start convection.
This is called the critical Rayleigh number Racr
Ra = ρgα∆ Td3
ρ = density; g = gravitation, d= layer thickness; α = thermal
expansivity; µ = dynamic viscosity; k = thermal diffusivity
OCE 661 Ra for fluids is on the order of ~ 1000. The greater the
number, the greater the “vigor” of convection. Ra for the
mantle is on the order of 107-109.
While mantle convection is very slow, it is considered vigorous
in hydrodynamic terms. It acts over huge distances against
extreme viscosity (~ 19 orders of magnitude greater than
Ok, Let’s consider simple symm...
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This document was uploaded on 01/26/2014.
- Winter '14