🚀 go-pugleaf

In article 2255@ucsu.Colorado.EDU, hatay@spot.Colorado.EDU (Ferhat F. Hatay) writes:
> 
> I want to derive the energy equation in its full 
> glory with true compressibility effects without
> an approximation like Boussinesq's.
> I am tempted to introduce a Mach number but I don't know
> how much sense this would make for geophysical/enviromental
> flows. Can you direct me to the proper references?
> 

Many basic fluids texts will at least show you the basic equation
with no approximations.  For a specific example on how to scale
such things, walk down the street a little ways to the JILA reading
room and look up my thesis and theses of Hurlburt, Merryfield, Xie
and all the other students of Juri Toomre who have done fully
compressible convection.

Basically, you do end up scaling velocities with the sound speed
at some point.  If you would rather not resolve acoustic waves,
you might think about doing an anelastic approximation which 
filters out acoustic waves, but still retains other aspects of
compressibility (buoyancy braking, etc.).  There are some 
references to anelastic convection simulations also in my 
thesis.

Good luck,

Phil


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