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Rayleighs theory is a search for the least

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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. T, This is called the critical Rayleigh number Racr This Ra = ρgα∆ Td3 Ra µk 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 Ra number, the greater the “vigor” of convection. Ra for the mantle is on the order of 107-109. mantle While mantle convection is very slow, it is considered vigorous While in hydrodynamic terms. It acts over huge distances against extreme viscosity (~ 19 orders of magnitude greater than molasses!). Ok, Let’s consider simple symm...
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