Deriving conservation of buoyancy from conservation of energy

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Wall
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Hi, all and thanks for your time.

I did read that the conservation of Buoyancy is an "alternative" conservation of energy under some hypothesis.

Can someone explain how do I start from the conservation of energy and find the conservation of buoyancy? Are there some corresponding mathematical passages?

Sorry for my bad English and thanks again!
 
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http://www.ifh.uni-karlsruhe.de/lehre/envflu_III/Downloads/models/IntegralPlumeModel/EFMIII-IntegralPlumeModel.pdf
 
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Thank you SO much! Do you have other documents about this problem? I'm working on plumes and trying to understand the dependence of the entrainment coefficient from the background rotation (but I'm a poor student). I did another post about entrainment.

I'm also trying to understand how to define mathematically the entrainment coefficient.

Thanks a lot!
 
Also, can I ask you some questions about that presentation you linked to me? thanks a lot!