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## Boussinesq approximation (buoyancy)In fluid dynamics, the ## Additional recommended knowledgeBoussinesq 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. The approximation's advantage arises because when
considering a flow of, say, warm and cold water of density
ρ - .
(Note that the denominator may be either density without affecting the result because the change would be of order
The mathematics of the flow is therefore simpler because the density ratio (ρ ## InversionsOne feature of Boussinesq flows is that they look the same when viewed upside-down, provided that the identities of the fluids are reversed. The Boussinesq approximation is For example, consider an open window in a warm room. The warm air inside is lighter than the cold air outside, which flows into the room and down towards the floor. Now imagine the opposite: a cold room exposed to warm outside air. Here the air flowing in moves up toward the ceiling. If the flow is Boussinesq (and the room is otherwise symmetrical), then viewing the cold room upside down is exactly the same as viewing the warm room right-way-round. This is because the only way density enters the problem is via the reduced gravity An example of a non-Boussinesq flow is bubbles rising in water. The behaviour of air bubbles rising in water is very different from the behaviour of water falling in air: in the former case rising bubbles tend to form hemispherical shells, while water falling in air splits into raindrops (at small length scales surface tension enters the problem and confuses the issue). |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Boussinesq_approximation_(buoyancy)". A list of authors is available in Wikipedia. |