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I've seen in some papers the definition of buoyancy flux as follows

$$B = g \frac{\rho_a-\rho_0}{\rho_0}Q$$

where $g$ is the gravity acceleration, $\rho_a$ is the density of the ambient fluid, $\rho_0$ is the density of the lighter fluid released into the ambient fluid from a point source, Q is the volumetric flow rate of the lighter fluid.

However I'm a bit confused with this definition as it has the units of $m^4/s^3$. But as it is the flux of buoyancy force, I think the formula should at least have mass with the unit in kg there. Can anyone help me out and let me know the accurate physical meaning of buoyancy flux?

The definition of the buoyancy flux in question can be found in:

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  • $\begingroup$ If you provide a link to the paper(s) you are reading, I will expand my answer with certainty. Without the citations though, it's mostly speculative... $\endgroup$ – tpg2114 Jul 20 '13 at 3:55
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Your confusion likely comes from it's use in equations. Really, this is the buoyancy flux per unit mass. In other words, the term in the governing equation will often appear as $\rho B$.

Without the specific paper(s) you are reading however, I cannot be sure of the definition.

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  • $\begingroup$ Many thanks for your comments! The definition can be found in Eq.(3-4) in the following publication: lboro.ac.uk/departments/cv/staff/docs/227/ch3/ch3.pdf And a similar one can be found in Eq. 5 from this paper: ctr.stanford.edu/ResBriefs99/basu.pdf The thing confuses me is physical meaning of buoyancy flux. As when we are talking about "flux", it appears to me that it should be some physical quantity per square meters per second, e.g. J/m^2.s for heat flux, and kg/m^2.s for mass flux. So what's the physical quantity associated with buoyancy flux? Is this thinking alright? $\endgroup$ – Mathew Jul 20 '13 at 10:25

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