Talk:Boussinesq approximation (buoyancy)

Hello everybody.

(newbie here). Anyone got examples of obviously non-Boussinesq flows that do not have the complication of surface energy?

Hello - I've just tidied up that section a little bit. The helical motion of rising air bubbles in water (due to pressure differences caused by helical boundary layer detachment) does not occur to the same extent for falling water droplets because the water droplets are significantly denser than the air. This isn't ideal though - because the inertial mass of the air bubble is significantly larger than it's actual mass due to the added mass of water than needs to be accelerated in order to accelerate the air bubble. I wasn't sure what the context of the last sentence was ("Boussinesq-approximation advantage: We need not to have temperature field to get dynamics.") so I removed it for reasons of clarity. Can anyone explain? Chrisjohnson 12:16, 16 March 2007 (UTC)

Inversions section misleading and irrelevant to understanding Boussinesq flows
(another newbie) The Inversions section is irrelevant to the Boussinesq approximation.

Use of reduced gravity is a special case of the Boussinesq approximation, which should be separated from the definition and referenced from the Boussinesq page. A continuously stratified fluid can be just as well approximated by the Boussinesq approximation. So Boussinesq physics should not be confused with reduced-gravity flows.

The example of beer bubbles and raindrops is misleading. Scaled with the right bubble/drop radii and velocities, these flows look much the same. Large raindrops form into hemispheric shapes and break up, like bubbles. The important quantity is the dynamic viscosity, of which density is only one factor. But arguing this is distracting, because it has little to do with the Boussinesq approximation. Far from being a helpful exposition on Boussinesq flows, this section should be removed. —Preceding unsigned comment added by Deszoeke (talk • contribs) 21:20, 27 November 2009 (UTC)

I think there is a strong possibility that the inversions section is only applicable when the domain doesn't vary in the direction of gravity. If you were to imagine a section of a cone with parallel top and bottom, and allow for sufficiently large Reynolds number that the nonlinear convective term comes into play, there is not necessarily reason to believe that switching the sign of the external forcing will simply switch the sign of the response. A nonlinear operator f need not obey f(-x) = - f(x). — Preceding unsigned comment added by 146.186.247.10 (talk) 19:40, 3 March 2014 (UTC)

The actual explanation for the change in the gravitational term in the momentum is missing
The missing link is that pressure is also approximated into p = p0 + p*, similar to \rho = \rho_0 + \rho^* and then all hydrostatic terms chancel to the momentum equation reduces and results in the shown approximation.