Boussinesq approximation

In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. It states that density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids.

Related Topics:
Fluid dynamics - Boussinesq - Inertia - Weight

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Boussinesq flows are common in nature (such as atmospheric fronts, oceanic circulation, katabatic winds), industry (dense gas dispersion, fume cupboard ventilation), and the built environment (natural ventilation, central heating). The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.

Related Topics:
Atmospheric front - Katabatic wind - Central heating

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The approximation's advantage arises because when

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considering a flow of, say, warm and cold water of density

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ho_1 and ho_2 one needs only consider a

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single density ho: the difference

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delta ho= ho_1- ho_2 is negligible.

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Dimensional analysis shows that, under these circumstances, the only sensible

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way that acceleration due to gravity g should enter into the equations of motion is in the reduced gravity g' where

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:g' = g{ ho_1- ho_2over { ho}}.

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(Note that the denominator may be either density without affecting the result because the change would be of order

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g(delta ho/ ho)^2). The most generally used dimensionless number would be the Richardson number.

Related Topics:
Dimensionless number - Richardson number

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The flow is therefore simpler because the density ratio ( ho_1/ ho_2---a dimensionless number) does not affect the flow: the Boussinesq approximation states that it may be assumed to be exactly one.

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