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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
    Commented Jul 20, 2013 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
    Commented Jul 20, 2013 at 10:25
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Think of the buoyancy of a parcel as minus the difference between its weight and that of the fluid it displaces. You experience the force of gravity as a downward force that determines your weight. A parcel (e.g. a Helium-filled balloon) that is less dense than it's surroundings is positively buoyant - it seems to have negative weight.

So the buoyancy flux through an area is really just the negative of the overall weight-flux. More dense air can be moving downwards, less dense upwards for a positive buoyancy flux. As previously stated, it is usually stated per unit mass, which is the cause of confusion (what's left is 'g', the acceleration due to gravity) and it's slightly confusing to talk about a flux of acceleration. This 'weight-flux' also represents a flux of potential energy, and the work done by the gravitational force in generating it produces kinetic energy; this is a vital term in the turbulent kinetic energy budget.

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